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This commit is contained in:
Harry Moffat 2004-08-05 17:49:46 +00:00
parent 84767d2772
commit 70fe2645ba
43 changed files with 8073 additions and 0 deletions
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3
ext/f2c_blas/.cvsignore Normal file
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*.d
.depends
Makefile

112
ext/f2c_blas/Makefile.in Executable file
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#/bin/sh
#
# $Source$
# $Author$
# $Revision$
# $Date$
# $License$
#
#/bin/sh
.SUFFIXES :
.SUFFIXES : .c .d .o
# the directory where the Cantera libraries are located
CANTERA_LIBDIR=@buildlib@
# the directory where Cantera include files may be found.
CANTERA_INCDIR=@ctroot@/build/include/cantera
# the C++ compiler
CXX = @CXX@
# the C compiler
CC = @CC@
# C++ compile flags
CXX_FLAGS = @CXXFLAGS@ $(CXX_OPT)
# Local include files
CXX_INCLUDES=-I../f2c_libs
# How to compile the dependency file
.c.d:
g++ -MM $(CXX_FLAGS) $(CXX_INCLUDES) $*.c > $*.d
# How to compile a C file
.c.o:
@CC@ -c $< @DEFS@ $(CXX_FLAGS) $(CXX_INCLUDES)
# -----------------------------------------------
BLASLIB = @buildlib@/libctblas.a
all: $(BLASLIB)
OBJS = \
dasum.o \
daxpy.o \
dcabs1.o \
dcopy.o \
ddot.o \
dgbmv.o \
dgemm.o \
dgemv.o \
dger.o \
dnrm2.o \
drot.o \
drotg.o \
drotm.o \
drotmg.o \
dsbmv.o \
dscal.o \
dsdot.o \
dspmv.o \
dspr.o \
dspr2.o \
dswap.o \
dsymm.o \
dsymv.o \
dsyr.o \
dsyr2.o \
dsyr2k.o \
dsyrk.o \
dtbmv.o \
dtbsv.o \
dtpmv.o \
dtpsv.o \
dtrmm.o \
dtrmv.o \
dtrsm.o \
dtrsv.o \
dzasum.o \
dznrm2.o \
idamax.o \
lsame.o \
xerbla.o
SRCS = $(OBJS:.o=.cpp)
# List of dependency files to be created
DEPENDS=$(OBJS:.o=.d)
# rule to make library
$(BLASLIB): $(OBJS)
@ARCHIVE@ $(BLASLIB) $(OBJS) > /dev/null
# ------------------------------------------------
# Utility Targets
clean:
$(RM) $(OBJS) $(BLASLIB) *.d .depends
# depends target
depends:
$(RM) *.d .depends
@MAKE@ .depends
.depends: $(DEPENDS)
cat *.d > .depends

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ext/f2c_blas/dasum.c Normal file
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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
doublereal dasum_(integer *n, doublereal *dx, integer *incx)
{
/* System generated locals */
integer i__1, i__2;
doublereal ret_val, d__1, d__2, d__3, d__4, d__5, d__6;
/* Local variables */
static integer i__, m;
static doublereal dtemp;
static integer nincx, mp1;
/* takes the sum of the absolute values.
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
Parameter adjustments */
--dx;
/* Function Body */
ret_val = 0.;
dtemp = 0.;
if (*n <= 0 || *incx <= 0) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
dtemp += (d__1 = dx[i__], abs(d__1));
/* L10: */
}
ret_val = dtemp;
return ret_val;
/* code for increment equal to 1
clean-up loop */
L20:
m = *n % 6;
if (m == 0) {
goto L40;
}
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
dtemp += (d__1 = dx[i__], abs(d__1));
/* L30: */
}
if (*n < 6) {
goto L60;
}
L40:
mp1 = m + 1;
i__2 = *n;
for (i__ = mp1; i__ <= i__2; i__ += 6) {
dtemp = dtemp + (d__1 = dx[i__], abs(d__1)) + (d__2 = dx[i__ + 1],
abs(d__2)) + (d__3 = dx[i__ + 2], abs(d__3)) + (d__4 = dx[i__
+ 3], abs(d__4)) + (d__5 = dx[i__ + 4], abs(d__5)) + (d__6 =
dx[i__ + 5], abs(d__6));
/* L50: */
}
L60:
ret_val = dtemp;
return ret_val;
} /* dasum_ */
#ifdef __cplusplus
}
#endif

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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int daxpy_(integer *n, doublereal *da, doublereal *dx,
integer *incx, doublereal *dy, integer *incy)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, m, ix, iy, mp1;
/* constant times a vector plus a vector. */
/* uses unrolled loops for increments equal to one. */
/* jack dongarra, linpack, 3/11/78. */
/* modified 12/3/93, array(1) declarations changed to array(*) */
/* Parameter adjustments */
--dy;
--dx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*da == 0.) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/* code for unequal increments or equal increments */
/* not equal to 1 */
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dy[iy] += *da * dx[ix];
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
/* clean-up loop */
L20:
m = *n % 4;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
dy[i__] += *da * dx[i__];
/* L30: */
}
if (*n < 4) {
return 0;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 4) {
dy[i__] += *da * dx[i__];
dy[i__ + 1] += *da * dx[i__ + 1];
dy[i__ + 2] += *da * dx[i__ + 2];
dy[i__ + 3] += *da * dx[i__ + 3];
/* L50: */
}
return 0;
} /* daxpy_ */
#ifdef __cplusplus
}
#endif

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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
doublereal dcabs1_(doublecomplex *z__)
{
/* System generated locals */
doublereal ret_val;
static doublecomplex equiv_0[1];
/* Local variables */
#define t ((doublereal *)equiv_0)
#define zz (equiv_0)
zz->r = z__->r, zz->i = z__->i;
ret_val = abs(t[0]) + abs(t[1]);
return ret_val;
} /* dcabs1_ */
#undef zz
#undef t
#ifdef __cplusplus
}
#endif

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ext/f2c_blas/dcopy.c Normal file
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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dcopy_(integer *n, doublereal *dx, integer *incx,
doublereal *dy, integer *incy)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, m, ix, iy, mp1;
/* copies a vector, x, to a vector, y.
uses unrolled loops for increments equal to one.
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
Parameter adjustments */
--dy;
--dx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/* code for unequal increments or equal increments
not equal to 1 */
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dy[iy] = dx[ix];
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1
clean-up loop */
L20:
m = *n % 7;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
dy[i__] = dx[i__];
/* L30: */
}
if (*n < 7) {
return 0;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 7) {
dy[i__] = dx[i__];
dy[i__ + 1] = dx[i__ + 1];
dy[i__ + 2] = dx[i__ + 2];
dy[i__ + 3] = dx[i__ + 3];
dy[i__ + 4] = dx[i__ + 4];
dy[i__ + 5] = dx[i__ + 5];
dy[i__ + 6] = dx[i__ + 6];
/* L50: */
}
return 0;
} /* dcopy_ */
#ifdef __cplusplus
}
#endif

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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy,
integer *incy)
{
/* System generated locals */
integer i__1;
doublereal ret_val;
/* Local variables */
static integer i__, m;
static doublereal dtemp;
static integer ix, iy, mp1;
/* forms the dot product of two vectors.
uses unrolled loops for increments equal to one.
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
Parameter adjustments */
--dy;
--dx;
/* Function Body */
ret_val = 0.;
dtemp = 0.;
if (*n <= 0) {
return ret_val;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/* code for unequal increments or equal increments
not equal to 1 */
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp += dx[ix] * dy[iy];
ix += *incx;
iy += *incy;
/* L10: */
}
ret_val = dtemp;
return ret_val;
/* code for both increments equal to 1
clean-up loop */
L20:
m = *n % 5;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp += dx[i__] * dy[i__];
/* L30: */
}
if (*n < 5) {
goto L60;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 5) {
dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + dx[
i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + dx[i__ +
4] * dy[i__ + 4];
/* L50: */
}
L60:
ret_val = dtemp;
return ret_val;
} /* ddot_ */
#ifdef __cplusplus
}
#endif

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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dgbmv_(char *trans, integer *m, integer *n, integer *kl,
integer *ku, doublereal *alpha, doublereal *a, integer *lda,
doublereal *x, integer *incx, doublereal *beta, doublereal *y,
integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
/* Local variables */
static integer info;
static doublereal temp;
static integer lenx, leny, i__, j, k;
extern logical lsame_(char *, char *);
static integer ix, iy, jx, jy, kx, ky;
extern /* Subroutine */ int xerbla_(char *, integer *);
static integer kup1;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DGBMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n band matrix, with kl sub-diagonals and ku super-diagonals.
Parameters
==========
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
TRANS = 'C' or 'c' y := alpha*A'*x + beta*y.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
KL - INTEGER.
On entry, KL specifies the number of sub-diagonals of the
matrix A. KL must satisfy 0 .le. KL.
Unchanged on exit.
KU - INTEGER.
On entry, KU specifies the number of super-diagonals of the
matrix A. KU must satisfy 0 .le. KU.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry, the leading ( kl + ku + 1 ) by n part of the
array A must contain the matrix of coefficients, supplied
column by column, with the leading diagonal of the matrix in
row ( ku + 1 ) of the array, the first super-diagonal
starting at position 2 in row ku, the first sub-diagonal
starting at position 1 in row ( ku + 2 ), and so on.
Elements in the array A that do not correspond to elements
in the band matrix (such as the top left ku by ku triangle)
are not referenced.
The following program segment will transfer a band matrix
from conventional full matrix storage to band storage:
DO 20, J = 1, N
K = KU + 1 - J
DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
A( K + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
( kl + ku + 1 ).
Unchanged on exit.
X - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
Before entry, the incremented array X must contain the
vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
Before entry, the incremented array Y must contain the
vector y. On exit, Y is overwritten by the updated vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*kl < 0) {
info = 4;
} else if (*ku < 0) {
info = 5;
} else if (*lda < *kl + *ku + 1) {
info = 8;
} else if (*incx == 0) {
info = 10;
} else if (*incy == 0) {
info = 13;
}
if (info != 0) {
xerbla_("DGBMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) {
return 0;
}
/* Set LENX and LENY, the lengths of the vectors x and y, and set
up the start points in X and Y. */
if (lsame_(trans, "N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through the band part of A.
First form y := beta*y. */
if (*beta != 1.) {
if (*incy == 1) {
if (*beta == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.;
/* L10: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.) {
return 0;
}
kup1 = *ku + 1;
if (lsame_(trans, "N")) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (*incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
k = kup1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__4 = min(i__5,i__6);
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
y[i__] += temp * a_ref(k + i__, j);
/* L50: */
}
}
jx += *incx;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
iy = ky;
k = kup1 - j;
/* Computing MAX */
i__4 = 1, i__2 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__3 = min(i__5,i__6);
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
y[iy] += temp * a_ref(k + i__, j);
iy += *incy;
/* L70: */
}
}
jx += *incx;
if (j > *ku) {
ky += *incy;
}
/* L80: */
}
}
} else {
/* Form y := alpha*A'*x + y. */
jy = ky;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.;
k = kup1 - j;
/* Computing MAX */
i__3 = 1, i__4 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__2 = min(i__5,i__6);
for (i__ = max(i__3,i__4); i__ <= i__2; ++i__) {
temp += a_ref(k + i__, j) * x[i__];
/* L90: */
}
y[jy] += *alpha * temp;
jy += *incy;
/* L100: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.;
ix = kx;
k = kup1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__4 = min(i__5,i__6);
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
temp += a_ref(k + i__, j) * x[ix];
ix += *incx;
/* L110: */
}
y[jy] += *alpha * temp;
jy += *incy;
if (j > *ku) {
kx += *incx;
}
/* L120: */
}
}
}
return 0;
/* End of DGBMV . */
} /* dgbmv_ */
#undef a_ref
#ifdef __cplusplus
}
#endif

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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer *
n, integer *k, doublereal *alpha, doublereal *a, integer *lda,
doublereal *b, integer *ldb, doublereal *beta, doublereal *c__,
integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer info;
static logical nota, notb;
static doublereal temp;
static integer i__, j, l, ncola;
extern logical lsame_(char *, char *);
static integer nrowa, nrowb;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define c___ref(a_1,a_2) c__[(a_2)*c_dim1 + a_1]
/* Purpose
=======
DGEMM performs one of the matrix-matrix operations
C := alpha*op( A )*op( B ) + beta*C,
where op( X ) is one of
op( X ) = X or op( X ) = X',
alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
Parameters
==========
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n', op( A ) = A.
TRANSA = 'T' or 't', op( A ) = A'.
TRANSA = 'C' or 'c', op( A ) = A'.
Unchanged on exit.
TRANSB - CHARACTER*1.
On entry, TRANSB specifies the form of op( B ) to be used in
the matrix multiplication as follows:
TRANSB = 'N' or 'n', op( B ) = B.
TRANSB = 'T' or 't', op( B ) = B'.
TRANSB = 'C' or 'c', op( B ) = B'.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix
op( A ) and of the matrix C. M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix
op( B ) and the number of columns of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry, K specifies the number of columns of the matrix
op( A ) and the number of rows of the matrix op( B ). K must
be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
k when TRANSA = 'N' or 'n', and is m otherwise.
Before entry with TRANSA = 'N' or 'n', the leading m by k
part of the array A must contain the matrix A, otherwise
the leading k by m part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANSA = 'N' or 'n' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, k ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
n when TRANSB = 'N' or 'n', and is k otherwise.
Before entry with TRANSB = 'N' or 'n', the leading k by n
part of the array B must contain the matrix B, otherwise
the leading n by k part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANSB = 'N' or 'n' then
LDB must be at least max( 1, k ), otherwise LDB must be at
least max( 1, n ).
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n matrix
( alpha*op( A )*op( B ) + beta*C ).
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Unchanged on exit.
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Set NOTA and NOTB as true if A and B respectively are not
transposed and set NROWA, NCOLA and NROWB as the number of rows
and columns of A and the number of rows of B respectively.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
/* Function Body */
nota = lsame_(transa, "N");
notb = lsame_(transb, "N");
if (nota) {
nrowa = *m;
ncola = *k;
} else {
nrowa = *k;
ncola = *m;
}
if (notb) {
nrowb = *k;
} else {
nrowb = *n;
}
/* Test the input parameters. */
info = 0;
if (! nota && ! lsame_(transa, "C") && ! lsame_(
transa, "T")) {
info = 1;
} else if (! notb && ! lsame_(transb, "C") && !
lsame_(transb, "T")) {
info = 2;
} else if (*m < 0) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*k < 0) {
info = 5;
} else if (*lda < max(1,nrowa)) {
info = 8;
} else if (*ldb < max(1,nrowb)) {
info = 10;
} else if (*ldc < max(1,*m)) {
info = 13;
}
if (info != 0) {
xerbla_("DGEMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
return 0;
}
/* And if alpha.eq.zero. */
if (*alpha == 0.) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L30: */
}
/* L40: */
}
}
return 0;
}
/* Start the operations. */
if (notb) {
if (nota) {
/* Form C := alpha*A*B + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L50: */
}
} else if (*beta != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L60: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (b_ref(l, j) != 0.) {
temp = *alpha * b_ref(l, j);
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c___ref(i__, j) = c___ref(i__, j) + temp * a_ref(
i__, l);
/* L70: */
}
}
/* L80: */
}
/* L90: */
}
} else {
/* Form C := alpha*A'*B + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a_ref(l, i__) * b_ref(l, j);
/* L100: */
}
if (*beta == 0.) {
c___ref(i__, j) = *alpha * temp;
} else {
c___ref(i__, j) = *alpha * temp + *beta * c___ref(i__,
j);
}
/* L110: */
}
/* L120: */
}
}
} else {
if (nota) {
/* Form C := alpha*A*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L130: */
}
} else if (*beta != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L140: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (b_ref(j, l) != 0.) {
temp = *alpha * b_ref(j, l);
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c___ref(i__, j) = c___ref(i__, j) + temp * a_ref(
i__, l);
/* L150: */
}
}
/* L160: */
}
/* L170: */
}
} else {
/* Form C := alpha*A'*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a_ref(l, i__) * b_ref(j, l);
/* L180: */
}
if (*beta == 0.) {
c___ref(i__, j) = *alpha * temp;
} else {
c___ref(i__, j) = *alpha * temp + *beta * c___ref(i__,
j);
}
/* L190: */
}
/* L200: */
}
}
}
return 0;
/* End of DGEMM . */
} /* dgemm_ */
#undef c___ref
#undef b_ref
#undef a_ref
#ifdef __cplusplus
}
#endif

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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dgemv_(char *trans, integer *m, integer *n, doublereal *
alpha, doublereal *a, integer *lda, doublereal *x, integer *incx,
doublereal *beta, doublereal *y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp;
static integer lenx, leny, i__, j;
extern logical lsame_(char *, char *);
static integer ix, iy, jx, jy, kx, ky;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DGEMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n matrix.
Parameters
==========
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
TRANS = 'C' or 'c' y := alpha*A'*x + beta*y.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
X - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
Before entry, the incremented array X must contain the
vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
Before entry with BETA non-zero, the incremented array Y
must contain the vector y. On exit, Y is overwritten by the
updated vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*lda < max(1,*m)) {
info = 6;
} else if (*incx == 0) {
info = 8;
} else if (*incy == 0) {
info = 11;
}
if (info != 0) {
xerbla_("DGEMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) {
return 0;
}
/* Set LENX and LENY, the lengths of the vectors x and y, and set
up the start points in X and Y. */
if (lsame_(trans, "N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
First form y := beta*y. */
if (*beta != 1.) {
if (*incy == 1) {
if (*beta == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.;
/* L10: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.) {
return 0;
}
if (lsame_(trans, "N")) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (*incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__] += temp * a_ref(i__, j);
/* L50: */
}
}
jx += *incx;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
iy = ky;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
y[iy] += temp * a_ref(i__, j);
iy += *incy;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
} else {
/* Form y := alpha*A'*x + y. */
jy = ky;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += a_ref(i__, j) * x[i__];
/* L90: */
}
y[jy] += *alpha * temp;
jy += *incy;
/* L100: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.;
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += a_ref(i__, j) * x[ix];
ix += *incx;
/* L110: */
}
y[jy] += *alpha * temp;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of DGEMV . */
} /* dgemv_ */
#undef a_ref
#ifdef __cplusplus
}
#endif

149
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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha,
doublereal *x, integer *incx, doublereal *y, integer *incy,
doublereal *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j, ix, jy, kx;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DGER performs the rank 1 operation
A := alpha*x*y' + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix.
Parameters
==========
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( m - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the m
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients. On exit, A is
overwritten by the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
info = 0;
if (*m < 0) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*m)) {
info = 9;
}
if (info != 0) {
xerbla_("DGER ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0.) {
return 0;
}
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through A. */
if (*incy > 0) {
jy = 1;
} else {
jy = 1 - (*n - 1) * *incy;
}
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (y[jy] != 0.) {
temp = *alpha * y[jy];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[i__] * temp;
/* L10: */
}
}
jy += *incy;
/* L20: */
}
} else {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*m - 1) * *incx;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (y[jy] != 0.) {
temp = *alpha * y[jy];
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[ix] * temp;
ix += *incx;
/* L30: */
}
}
jy += *incy;
/* L40: */
}
}
return 0;
/* End of DGER . */
} /* dger_ */
#undef a_ref
#ifdef __cplusplus
}
#endif

68
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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
doublereal dnrm2_(integer *n, doublereal *x, integer *incx)
{
/* The following loop is equivalent to this call to the LAPACK
auxiliary routine:
CALL DLASSQ( N, X, INCX, SCALE, SSQ ) */
/* System generated locals */
integer i__1, i__2;
doublereal ret_val, d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static doublereal norm, scale, absxi;
static integer ix;
static doublereal ssq;
/* DNRM2 returns the euclidean norm of a vector via the function
name, so that
DNRM2 := sqrt( x'*x )
-- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to DLASSQ.
Sven Hammarling, Nag Ltd.
Parameter adjustments */
--x;
/* Function Body */
if (*n < 1 || *incx < 1) {
norm = 0.;
} else if (*n == 1) {
norm = abs(x[1]);
} else {
scale = 0.;
ssq = 1.;
i__1 = (*n - 1) * *incx + 1;
i__2 = *incx;
for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
if (x[ix] != 0.) {
absxi = (d__1 = x[ix], abs(d__1));
if (scale < absxi) {
/* Computing 2nd power */
d__1 = scale / absxi;
ssq = ssq * (d__1 * d__1) + 1.;
scale = absxi;
} else {
/* Computing 2nd power */
d__1 = absxi / scale;
ssq += d__1 * d__1;
}
}
/* L10: */
}
norm = scale * sqrt(ssq);
}
ret_val = norm;
return ret_val;
/* End of DNRM2. */
} /* dnrm2_ */
#ifdef __cplusplus
}
#endif

62
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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int drot_(integer *n, doublereal *dx, integer *incx,
doublereal *dy, integer *incy, doublereal *c__, doublereal *s)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__;
static doublereal dtemp;
static integer ix, iy;
/* applies a plane rotation.
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
Parameter adjustments */
--dy;
--dx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/* code for unequal increments or equal increments not equal
to 1 */
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp = *c__ * dx[ix] + *s * dy[iy];
dy[iy] = *c__ * dy[iy] - *s * dx[ix];
dx[ix] = dtemp;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp = *c__ * dx[i__] + *s * dy[i__];
dy[i__] = *c__ * dy[i__] - *s * dx[i__];
dx[i__] = dtemp;
/* L30: */
}
return 0;
} /* drot_ */
#ifdef __cplusplus
}
#endif

57
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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int drotg_(doublereal *da, doublereal *db, doublereal *c__,
doublereal *s)
{
/* Table of constant values */
static doublereal c_b4 = 1.;
/* System generated locals */
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal), d_sign(doublereal *, doublereal *);
/* Local variables */
static doublereal r__, scale, z__, roe;
/* construct givens plane rotation.
jack dongarra, linpack, 3/11/78. */
roe = *db;
if (abs(*da) > abs(*db)) {
roe = *da;
}
scale = abs(*da) + abs(*db);
if (scale != 0.) {
goto L10;
}
*c__ = 1.;
*s = 0.;
r__ = 0.;
z__ = 0.;
goto L20;
L10:
/* Computing 2nd power */
d__1 = *da / scale;
/* Computing 2nd power */
d__2 = *db / scale;
r__ = scale * sqrt(d__1 * d__1 + d__2 * d__2);
r__ = d_sign(&c_b4, &roe) * r__;
*c__ = *da / r__;
*s = *db / r__;
z__ = 1.;
if (abs(*da) > abs(*db)) {
z__ = *s;
}
if (abs(*db) >= abs(*da) && *c__ != 0.) {
z__ = 1. / *c__;
}
L20:
*da = r__;
*db = z__;
return 0;
} /* drotg_ */
#ifdef __cplusplus
}
#endif

183
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/* drotm.f -- translated by f2c (version 20031025).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int drotm_(integer *n, doublereal *dx, integer *incx,
doublereal *dy, integer *incy, doublereal *dparam)
{
/* Initialized data */
static doublereal zero = 0.;
static doublereal two = 2.;
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer i__;
static doublereal w, z__;
static integer kx, ky;
static doublereal dh11, dh12, dh22, dh21, dflag;
static integer nsteps;
/* APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX */
/* (DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN */
/* (DY**T) */
/* DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE */
/* LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY. */
/* WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */
/* DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 */
/* (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) */
/* H=( ) ( ) ( ) ( ) */
/* (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). */
/* SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM. */
/* Parameter adjustments */
--dparam;
--dy;
--dx;
/* Function Body */
dflag = dparam[1];
if (*n <= 0 || dflag + two == zero) {
goto L140;
}
if (! (*incx == *incy && *incx > 0)) {
goto L70;
}
nsteps = *n * *incx;
if (dflag < 0.) {
goto L50;
} else if (dflag == 0) {
goto L10;
} else {
goto L30;
}
L10:
dh12 = dparam[4];
dh21 = dparam[3];
i__1 = nsteps;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
w = dx[i__];
z__ = dy[i__];
dx[i__] = w + z__ * dh12;
dy[i__] = w * dh21 + z__;
/* L20: */
}
goto L140;
L30:
dh11 = dparam[2];
dh22 = dparam[5];
i__2 = nsteps;
i__1 = *incx;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
w = dx[i__];
z__ = dy[i__];
dx[i__] = w * dh11 + z__;
dy[i__] = -w + dh22 * z__;
/* L40: */
}
goto L140;
L50:
dh11 = dparam[2];
dh12 = dparam[4];
dh21 = dparam[3];
dh22 = dparam[5];
i__1 = nsteps;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
w = dx[i__];
z__ = dy[i__];
dx[i__] = w * dh11 + z__ * dh12;
dy[i__] = w * dh21 + z__ * dh22;
/* L60: */
}
goto L140;
L70:
kx = 1;
ky = 1;
if (*incx < 0) {
kx = (1 - *n) * *incx + 1;
}
if (*incy < 0) {
ky = (1 - *n) * *incy + 1;
}
if (dflag < 0.) {
goto L120;
} else if (dflag == 0) {
goto L80;
} else {
goto L100;
}
L80:
dh12 = dparam[4];
dh21 = dparam[3];
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
w = dx[kx];
z__ = dy[ky];
dx[kx] = w + z__ * dh12;
dy[ky] = w * dh21 + z__;
kx += *incx;
ky += *incy;
/* L90: */
}
goto L140;
L100:
dh11 = dparam[2];
dh22 = dparam[5];
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
w = dx[kx];
z__ = dy[ky];
dx[kx] = w * dh11 + z__;
dy[ky] = -w + dh22 * z__;
kx += *incx;
ky += *incy;
/* L110: */
}
goto L140;
L120:
dh11 = dparam[2];
dh12 = dparam[4];
dh21 = dparam[3];
dh22 = dparam[5];
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
w = dx[kx];
z__ = dy[ky];
dx[kx] = w * dh11 + z__ * dh12;
dy[ky] = w * dh21 + z__ * dh22;
kx += *incx;
ky += *incy;
/* L130: */
}
L140:
return 0;
} /* drotm_ */
#ifdef __cplusplus
}
#endif

265
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/* drotmg.f -- translated by f2c (version 20031025).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int drotmg_(doublereal *dd1, doublereal *dd2, doublereal *
dx1, doublereal *dy1, doublereal *dparam)
{
/* Initialized data */
static doublereal zero = 0.;
static doublereal one = 1.;
static doublereal two = 2.;
static doublereal gam = 4096.;
static doublereal gamsq = 16777216.;
static doublereal rgamsq = 5.9604645e-8;
/* Format strings */
static char fmt_120[] = "";
static char fmt_150[] = "";
static char fmt_180[] = "";
static char fmt_210[] = "";
/* System generated locals */
doublereal d__1;
/* Local variables */
static doublereal du, dp1, dp2, dq2, dq1, dh11, dh21, dh12, dh22;
static integer igo;
static doublereal dflag, dtemp;
/* Assigned format variables */
static char *igo_fmt;
/* CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS */
/* THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)* */
/* DY2)**T. */
/* WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */
/* DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 */
/* (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) */
/* H=( ) ( ) ( ) ( ) */
/* (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). */
/* LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22 */
/* RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE */
/* VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.) */
/* THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE */
/* INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE */
/* OF DD1 AND DD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. */
/* Parameter adjustments */
--dparam;
/* Function Body */
if (! (*dd1 < zero)) {
goto L10;
}
/* GO ZERO-H-D-AND-DX1.. */
goto L60;
L10:
/* CASE-DD1-NONNEGATIVE */
dp2 = *dd2 * *dy1;
if (! (dp2 == zero)) {
goto L20;
}
dflag = -two;
goto L260;
/* REGULAR-CASE.. */
L20:
dp1 = *dd1 * *dx1;
dq2 = dp2 * *dy1;
dq1 = dp1 * *dx1;
if (! (abs(dq1) > abs(dq2))) {
goto L40;
}
dh21 = -(*dy1) / *dx1;
dh12 = dp2 / dp1;
du = one - dh12 * dh21;
if (! (du <= zero)) {
goto L30;
}
/* GO ZERO-H-D-AND-DX1.. */
goto L60;
L30:
dflag = zero;
*dd1 /= du;
*dd2 /= du;
*dx1 *= du;
/* GO SCALE-CHECK.. */
goto L100;
L40:
if (! (dq2 < zero)) {
goto L50;
}
/* GO ZERO-H-D-AND-DX1.. */
goto L60;
L50:
dflag = one;
dh11 = dp1 / dp2;
dh22 = *dx1 / *dy1;
du = one + dh11 * dh22;
dtemp = *dd2 / du;
*dd2 = *dd1 / du;
*dd1 = dtemp;
*dx1 = *dy1 * du;
/* GO SCALE-CHECK */
goto L100;
/* PROCEDURE..ZERO-H-D-AND-DX1.. */
L60:
dflag = -one;
dh11 = zero;
dh12 = zero;
dh21 = zero;
dh22 = zero;
*dd1 = zero;
*dd2 = zero;
*dx1 = zero;
/* RETURN.. */
goto L220;
/* PROCEDURE..FIX-H.. */
L70:
if (! (dflag >= zero)) {
goto L90;
}
if (! (dflag == zero)) {
goto L80;
}
dh11 = one;
dh22 = one;
dflag = -one;
goto L90;
L80:
dh21 = -one;
dh12 = one;
dflag = -one;
L90:
switch (igo) {
case 0: goto L120;
case 1: goto L150;
case 2: goto L180;
case 3: goto L210;
}
/* PROCEDURE..SCALE-CHECK */
L100:
L110:
if (! (*dd1 <= rgamsq)) {
goto L130;
}
if (*dd1 == zero) {
goto L160;
}
igo = 0;
igo_fmt = fmt_120;
/* FIX-H.. */
goto L70;
L120:
/* Computing 2nd power */
d__1 = gam;
*dd1 *= d__1 * d__1;
*dx1 /= gam;
dh11 /= gam;
dh12 /= gam;
goto L110;
L130:
L140:
if (! (*dd1 >= gamsq)) {
goto L160;
}
igo = 1;
igo_fmt = fmt_150;
/* FIX-H.. */
goto L70;
L150:
/* Computing 2nd power */
d__1 = gam;
*dd1 /= d__1 * d__1;
*dx1 *= gam;
dh11 *= gam;
dh12 *= gam;
goto L140;
L160:
L170:
if (! (abs(*dd2) <= rgamsq)) {
goto L190;
}
if (*dd2 == zero) {
goto L220;
}
igo = 2;
igo_fmt = fmt_180;
/* FIX-H.. */
goto L70;
L180:
/* Computing 2nd power */
d__1 = gam;
*dd2 *= d__1 * d__1;
dh21 /= gam;
dh22 /= gam;
goto L170;
L190:
L200:
if (! (abs(*dd2) >= gamsq)) {
goto L220;
}
igo = 3;
igo_fmt = fmt_210;
/* FIX-H.. */
goto L70;
L210:
/* Computing 2nd power */
d__1 = gam;
*dd2 /= d__1 * d__1;
dh21 *= gam;
dh22 *= gam;
goto L200;
L220:
if (dflag < 0.) {
goto L250;
} else if (dflag == 0) {
goto L230;
} else {
goto L240;
}
L230:
dparam[3] = dh21;
dparam[4] = dh12;
goto L260;
L240:
dparam[2] = dh11;
dparam[5] = dh22;
goto L260;
L250:
dparam[2] = dh11;
dparam[3] = dh21;
dparam[4] = dh12;
dparam[5] = dh22;
L260:
dparam[1] = dflag;
return 0;
} /* drotmg_ */
#ifdef __cplusplus
}
#endif

299
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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dsbmv_(char *uplo, integer *n, integer *k, doublereal *
alpha, doublereal *a, integer *lda, doublereal *x, integer *incx,
doublereal *beta, doublereal *y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer info;
static doublereal temp1, temp2;
static integer i__, j, l;
extern logical lsame_(char *, char *);
static integer kplus1, ix, iy, jx, jy, kx, ky;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DSBMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric band matrix, with k super-diagonals.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the band matrix A is being supplied as
follows:
UPLO = 'U' or 'u' The upper triangular part of A is
being supplied.
UPLO = 'L' or 'l' The lower triangular part of A is
being supplied.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
K - INTEGER.
On entry, K specifies the number of super-diagonals of the
matrix A. K must satisfy 0 .le. K.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
by n part of the array A must contain the upper triangular
band part of the symmetric matrix, supplied column by
column, with the leading diagonal of the matrix in row
( k + 1 ) of the array, the first super-diagonal starting at
position 2 in row k, and so on. The top left k by k triangle
of the array A is not referenced.
The following program segment will transfer the upper
triangular part of a symmetric band matrix from conventional
full matrix storage to band storage:
DO 20, J = 1, N
M = K + 1 - J
DO 10, I = MAX( 1, J - K ), J
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
by n part of the array A must contain the lower triangular
band part of the symmetric matrix, supplied column by
column, with the leading diagonal of the matrix in row 1 of
the array, the first sub-diagonal starting at position 1 in
row 2, and so on. The bottom right k by k triangle of the
array A is not referenced.
The following program segment will transfer the lower
triangular part of a symmetric band matrix from conventional
full matrix storage to band storage:
DO 20, J = 1, N
M = 1 - J
DO 10, I = J, MIN( N, J + K )
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
( k + 1 ).
Unchanged on exit.
X - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the
vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.
Unchanged on exit.
Y - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the
vector y. On exit, Y is overwritten by the updated vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*k < 0) {
info = 3;
} else if (*lda < *k + 1) {
info = 6;
} else if (*incx == 0) {
info = 8;
} else if (*incy == 0) {
info = 11;
}
if (info != 0) {
xerbla_("DSBMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0. && *beta == 1.) {
return 0;
}
/* Set up the start points in X and Y. */
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
/* Start the operations. In this version the elements of the array A
are accessed sequentially with one pass through A.
First form y := beta*y. */
if (*beta != 1.) {
if (*incy == 1) {
if (*beta == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.;
/* L10: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.) {
return 0;
}
if (lsame_(uplo, "U")) {
/* Form y when upper triangle of A is stored. */
kplus1 = *k + 1;
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.;
l = kplus1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__4 = j - 1;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
y[i__] += temp1 * a_ref(l + i__, j);
temp2 += a_ref(l + i__, j) * x[i__];
/* L50: */
}
y[j] = y[j] + temp1 * a_ref(kplus1, j) + *alpha * temp2;
/* L60: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.;
ix = kx;
iy = ky;
l = kplus1 - j;
/* Computing MAX */
i__4 = 1, i__2 = j - *k;
i__3 = j - 1;
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
y[iy] += temp1 * a_ref(l + i__, j);
temp2 += a_ref(l + i__, j) * x[ix];
ix += *incx;
iy += *incy;
/* L70: */
}
y[jy] = y[jy] + temp1 * a_ref(kplus1, j) + *alpha * temp2;
jx += *incx;
jy += *incy;
if (j > *k) {
kx += *incx;
ky += *incy;
}
/* L80: */
}
}
} else {
/* Form y when lower triangle of A is stored. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.;
y[j] += temp1 * a_ref(1, j);
l = 1 - j;
/* Computing MIN */
i__4 = *n, i__2 = j + *k;
i__3 = min(i__4,i__2);
for (i__ = j + 1; i__ <= i__3; ++i__) {
y[i__] += temp1 * a_ref(l + i__, j);
temp2 += a_ref(l + i__, j) * x[i__];
/* L90: */
}
y[j] += *alpha * temp2;
/* L100: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.;
y[jy] += temp1 * a_ref(1, j);
l = 1 - j;
ix = jx;
iy = jy;
/* Computing MIN */
i__4 = *n, i__2 = j + *k;
i__3 = min(i__4,i__2);
for (i__ = j + 1; i__ <= i__3; ++i__) {
ix += *incx;
iy += *incy;
y[iy] += temp1 * a_ref(l + i__, j);
temp2 += a_ref(l + i__, j) * x[ix];
/* L110: */
}
y[jy] += *alpha * temp2;
jx += *incx;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of DSBMV . */
} /* dsbmv_ */
#undef a_ref
#ifdef __cplusplus
}
#endif

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#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx,
integer *incx)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer i__, m, nincx, mp1;
/* scales a vector by a constant.
uses unrolled loops for increment equal to one.
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
Parameter adjustments */
--dx;
/* Function Body */
if (*n <= 0 || *incx <= 0) {
return 0;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
dx[i__] = *da * dx[i__];
/* L10: */
}
return 0;
/* code for increment equal to 1
clean-up loop */
L20:
m = *n % 5;
if (m == 0) {
goto L40;
}
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
dx[i__] = *da * dx[i__];
/* L30: */
}
if (*n < 5) {
return 0;
}
L40:
mp1 = m + 1;
i__2 = *n;
for (i__ = mp1; i__ <= i__2; i__ += 5) {
dx[i__] = *da * dx[i__];
dx[i__ + 1] = *da * dx[i__ + 1];
dx[i__ + 2] = *da * dx[i__ + 2];
dx[i__ + 3] = *da * dx[i__ + 3];
dx[i__ + 4] = *da * dx[i__ + 4];
/* L50: */
}
return 0;
} /* dscal_ */

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/* dsdot.f -- translated by f2c (version 20031025).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* DECK DSDOT */
doublereal dsdot_(integer *n, real *sx, integer *incx, real *sy, integer *
incy)
{
/* System generated locals */
integer i__1, i__2;
doublereal ret_val;
/* Local variables */
static integer i__, ns, kx, ky;
/* ***BEGIN PROLOGUE DSDOT */
/* ***PURPOSE Compute the inner product of two vectors with extended */
/* precision accumulation and result. */
/* ***LIBRARY SLATEC (BLAS) */
/* ***CATEGORY D1A4 */
/* ***TYPE DOUBLE PRECISION (DSDOT-D, DCDOT-C) */
/* ***KEYWORDS BLAS, COMPLEX VECTORS, DOT PRODUCT, INNER PRODUCT, */
/* LINEAR ALGEBRA, VECTOR */
/* ***AUTHOR Lawson, C. L., (JPL) */
/* Hanson, R. J., (SNLA) */
/* Kincaid, D. R., (U. of Texas) */
/* Krogh, F. T., (JPL) */
/* ***DESCRIPTION */
/* B L A S Subprogram */
/* Description of Parameters */
/* --Input-- */
/* N number of elements in input vector(s) */
/* SX single precision vector with N elements */
/* INCX storage spacing between elements of SX */
/* SY single precision vector with N elements */
/* INCY storage spacing between elements of SY */
/* --Output-- */
/* DSDOT double precision dot product (zero if N.LE.0) */
/* Returns D.P. dot product accumulated in D.P., for S.P. SX and SY */
/* DSDOT = sum for I = 0 to N-1 of SX(LX+I*INCX) * SY(LY+I*INCY), */
/* where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is */
/* defined in a similar way using INCY. */
/* ***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. */
/* Krogh, Basic linear algebra subprograms for Fortran */
/* usage, Algorithm No. 539, Transactions on Mathematical */
/* Software 5, 3 (September 1979), pp. 308-323. */
/* ***ROUTINES CALLED (NONE) */
/* ***REVISION HISTORY (YYMMDD) */
/* 791001 DATE WRITTEN */
/* 890831 Modified array declarations. (WRB) */
/* 890831 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 920310 Corrected definition of LX in DESCRIPTION. (WRB) */
/* 920501 Reformatted the REFERENCES section. (WRB) */
/* ***END PROLOGUE DSDOT */
/* ***FIRST EXECUTABLE STATEMENT DSDOT */
/* Parameter adjustments */
--sy;
--sx;
/* Function Body */
ret_val = 0.;
if (*n <= 0) {
return ret_val;
}
if (*incx == *incy && *incx > 0) {
goto L20;
}
/* Code for unequal or nonpositive increments. */
kx = 1;
ky = 1;
if (*incx < 0) {
kx = (1 - *n) * *incx + 1;
}
if (*incy < 0) {
ky = (1 - *n) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
ret_val += (doublereal) sx[kx] * (doublereal) sy[ky];
kx += *incx;
ky += *incy;
/* L10: */
}
return ret_val;
/* Code for equal, positive, non-unit increments. */
L20:
ns = *n * *incx;
i__1 = ns;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
ret_val += (doublereal) sx[i__] * (doublereal) sy[i__];
/* L30: */
}
return ret_val;
} /* dsdot_ */
#ifdef __cplusplus
}
#endif

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#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int dspmv_(char *uplo, integer *n, doublereal *alpha,
doublereal *ap, doublereal *x, integer *incx, doublereal *beta,
doublereal *y, integer *incy)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp1, temp2;
static integer i__, j, k;
extern logical lsame_(char *, char *);
static integer kk, ix, iy, jx, jy, kx, ky;
extern /* Subroutine */ int xerbla_(char *, integer *);
/* Purpose
=======
DSPMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric matrix, supplied in packed form.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the matrix A is supplied in the packed
array AP as follows:
UPLO = 'U' or 'u' The upper triangular part of A is
supplied in AP.
UPLO = 'L' or 'l' The lower triangular part of A is
supplied in AP.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
AP - DOUBLE PRECISION array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = 'U' or 'u', the array AP must
contain the upper triangular part of the symmetric matrix
packed sequentially, column by column, so that AP( 1 )
contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
and a( 2, 2 ) respectively, and so on.
Before entry with UPLO = 'L' or 'l', the array AP must
contain the lower triangular part of the symmetric matrix
packed sequentially, column by column, so that AP( 1 )
contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
and a( 3, 1 ) respectively, and so on.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y. On exit, Y is overwritten by the updated
vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
--y;
--x;
--ap;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 6;
} else if (*incy == 0) {
info = 9;
}
if (info != 0) {
xerbla_("DSPMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0. && *beta == 1.) {
return 0;
}
/* Set up the start points in X and Y. */
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
/* Start the operations. In this version the elements of the array AP
are accessed sequentially with one pass through AP.
First form y := beta*y. */
if (*beta != 1.) {
if (*incy == 1) {
if (*beta == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.;
/* L10: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.) {
return 0;
}
kk = 1;
if (lsame_(uplo, "U")) {
/* Form y when AP contains the upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.;
k = kk;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__] += temp1 * ap[k];
temp2 += ap[k] * x[i__];
++k;
/* L50: */
}
y[j] = y[j] + temp1 * ap[kk + j - 1] + *alpha * temp2;
kk += j;
/* L60: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.;
ix = kx;
iy = ky;
i__2 = kk + j - 2;
for (k = kk; k <= i__2; ++k) {
y[iy] += temp1 * ap[k];
temp2 += ap[k] * x[ix];
ix += *incx;
iy += *incy;
/* L70: */
}
y[jy] = y[jy] + temp1 * ap[kk + j - 1] + *alpha * temp2;
jx += *incx;
jy += *incy;
kk += j;
/* L80: */
}
}
} else {
/* Form y when AP contains the lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.;
y[j] += temp1 * ap[kk];
k = kk + 1;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
y[i__] += temp1 * ap[k];
temp2 += ap[k] * x[i__];
++k;
/* L90: */
}
y[j] += *alpha * temp2;
kk += *n - j + 1;
/* L100: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.;
y[jy] += temp1 * ap[kk];
ix = jx;
iy = jy;
i__2 = kk + *n - j;
for (k = kk + 1; k <= i__2; ++k) {
ix += *incx;
iy += *incy;
y[iy] += temp1 * ap[k];
temp2 += ap[k] * x[ix];
/* L110: */
}
y[jy] += *alpha * temp2;
jx += *incx;
jy += *incy;
kk += *n - j + 1;
/* L120: */
}
}
}
return 0;
/* End of DSPMV . */
} /* dspmv_ */

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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dspr_(char *uplo, integer *n, doublereal *alpha,
doublereal *x, integer *incx, doublereal *ap)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j, k;
extern logical lsame_(char *, char *);
static integer kk, ix, jx, kx;
extern /* Subroutine */ int xerbla_(char *, integer *);
/* Purpose
=======
DSPR performs the symmetric rank 1 operation
A := alpha*x*x' + A,
where alpha is a real scalar, x is an n element vector and A is an
n by n symmetric matrix, supplied in packed form.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the matrix A is supplied in the packed
array AP as follows:
UPLO = 'U' or 'u' The upper triangular part of A is
supplied in AP.
UPLO = 'L' or 'l' The lower triangular part of A is
supplied in AP.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
AP - DOUBLE PRECISION array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = 'U' or 'u', the array AP must
contain the upper triangular part of the symmetric matrix
packed sequentially, column by column, so that AP( 1 )
contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
and a( 2, 2 ) respectively, and so on. On exit, the array
AP is overwritten by the upper triangular part of the
updated matrix.
Before entry with UPLO = 'L' or 'l', the array AP must
contain the lower triangular part of the symmetric matrix
packed sequentially, column by column, so that AP( 1 )
contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
and a( 3, 1 ) respectively, and so on. On exit, the array
AP is overwritten by the lower triangular part of the
updated matrix.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
--ap;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
}
if (info != 0) {
xerbla_("DSPR ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0.) {
return 0;
}
/* Set the start point in X if the increment is not unity. */
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/* Start the operations. In this version the elements of the array AP
are accessed sequentially with one pass through AP. */
kk = 1;
if (lsame_(uplo, "U")) {
/* Form A when upper triangle is stored in AP. */
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
temp = *alpha * x[j];
k = kk;
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
ap[k] += x[i__] * temp;
++k;
/* L10: */
}
}
kk += j;
/* L20: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
ix = kx;
i__2 = kk + j - 1;
for (k = kk; k <= i__2; ++k) {
ap[k] += x[ix] * temp;
ix += *incx;
/* L30: */
}
}
jx += *incx;
kk += j;
/* L40: */
}
}
} else {
/* Form A when lower triangle is stored in AP. */
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
temp = *alpha * x[j];
k = kk;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
ap[k] += x[i__] * temp;
++k;
/* L50: */
}
}
kk = kk + *n - j + 1;
/* L60: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
ix = jx;
i__2 = kk + *n - j;
for (k = kk; k <= i__2; ++k) {
ap[k] += x[ix] * temp;
ix += *incx;
/* L70: */
}
}
jx += *incx;
kk = kk + *n - j + 1;
/* L80: */
}
}
}
return 0;
/* End of DSPR . */
} /* dspr_ */
#ifdef __cplusplus
}
#endif

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#include "blaswrap.h"
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dspr2_(char *uplo, integer *n, doublereal *alpha,
doublereal *x, integer *incx, doublereal *y, integer *incy,
doublereal *ap)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp1, temp2;
static integer i__, j, k;
extern logical lsame_(char *, char *);
static integer kk, ix, iy, jx, jy, kx, ky;
extern /* Subroutine */ int xerbla_(char *, integer *);
/* Purpose
=======
DSPR2 performs the symmetric rank 2 operation
A := alpha*x*y' + alpha*y*x' + A,
where alpha is a scalar, x and y are n element vectors and A is an
n by n symmetric matrix, supplied in packed form.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the matrix A is supplied in the packed
array AP as follows:
UPLO = 'U' or 'u' The upper triangular part of A is
supplied in AP.
UPLO = 'L' or 'l' The lower triangular part of A is
supplied in AP.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
AP - DOUBLE PRECISION array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = 'U' or 'u', the array AP must
contain the upper triangular part of the symmetric matrix
packed sequentially, column by column, so that AP( 1 )
contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
and a( 2, 2 ) respectively, and so on. On exit, the array
AP is overwritten by the upper triangular part of the
updated matrix.
Before entry with UPLO = 'L' or 'l', the array AP must
contain the lower triangular part of the symmetric matrix
packed sequentially, column by column, so that AP( 1 )
contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
and a( 3, 1 ) respectively, and so on. On exit, the array
AP is overwritten by the lower triangular part of the
updated matrix.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
--ap;
--y;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
}
if (info != 0) {
xerbla_("DSPR2 ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0.) {
return 0;
}
/* Set up the start points in X and Y if the increments are not both
unity. */
if (*incx != 1 || *incy != 1) {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
jx = kx;
jy = ky;
}
/* Start the operations. In this version the elements of the array AP
are accessed sequentially with one pass through AP. */
kk = 1;
if (lsame_(uplo, "U")) {
/* Form A when upper triangle is stored in AP. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0. || y[j] != 0.) {
temp1 = *alpha * y[j];
temp2 = *alpha * x[j];
k = kk;
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
ap[k] = ap[k] + x[i__] * temp1 + y[i__] * temp2;
++k;
/* L10: */
}
}
kk += j;
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0. || y[jy] != 0.) {
temp1 = *alpha * y[jy];
temp2 = *alpha * x[jx];
ix = kx;
iy = ky;
i__2 = kk + j - 1;
for (k = kk; k <= i__2; ++k) {
ap[k] = ap[k] + x[ix] * temp1 + y[iy] * temp2;
ix += *incx;
iy += *incy;
/* L30: */
}
}
jx += *incx;
jy += *incy;
kk += j;
/* L40: */
}
}
} else {
/* Form A when lower triangle is stored in AP. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0. || y[j] != 0.) {
temp1 = *alpha * y[j];
temp2 = *alpha * x[j];
k = kk;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
ap[k] = ap[k] + x[i__] * temp1 + y[i__] * temp2;
++k;
/* L50: */
}
}
kk = kk + *n - j + 1;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0. || y[jy] != 0.) {
temp1 = *alpha * y[jy];
temp2 = *alpha * x[jx];
ix = jx;
iy = jy;
i__2 = kk + *n - j;
for (k = kk; k <= i__2; ++k) {
ap[k] = ap[k] + x[ix] * temp1 + y[iy] * temp2;
ix += *incx;
iy += *incy;
/* L70: */
}
}
jx += *incx;
jy += *incy;
kk = kk + *n - j + 1;
/* L80: */
}
}
}
return 0;
/* End of DSPR2 . */
} /* dspr2_ */
#ifdef __cplusplus
}
#endif

87
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx,
doublereal *dy, integer *incy)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, m;
static doublereal dtemp;
static integer ix, iy, mp1;
/* interchanges two vectors.
uses unrolled loops for increments equal one.
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
Parameter adjustments */
--dy;
--dx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/* code for unequal increments or equal increments not equal
to 1 */
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp = dx[ix];
dx[ix] = dy[iy];
dy[iy] = dtemp;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1
clean-up loop */
L20:
m = *n % 3;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp = dx[i__];
dx[i__] = dy[i__];
dy[i__] = dtemp;
/* L30: */
}
if (*n < 3) {
return 0;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 3) {
dtemp = dx[i__];
dx[i__] = dy[i__];
dy[i__] = dtemp;
dtemp = dx[i__ + 1];
dx[i__ + 1] = dy[i__ + 1];
dy[i__ + 1] = dtemp;
dtemp = dx[i__ + 2];
dx[i__ + 2] = dy[i__ + 2];
dy[i__ + 2] = dtemp;
/* L50: */
}
return 0;
} /* dswap_ */
#ifdef _cpluscplus
}
#endif

298
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dsymm_(char *side, char *uplo, integer *m, integer *n,
doublereal *alpha, doublereal *a, integer *lda, doublereal *b,
integer *ldb, doublereal *beta, doublereal *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer info;
static doublereal temp1, temp2;
static integer i__, j, k;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define c___ref(a_1,a_2) c__[(a_2)*c_dim1 + a_1]
/* Purpose
=======
DSYMM performs one of the matrix-matrix operations
C := alpha*A*B + beta*C,
or
C := alpha*B*A + beta*C,
where alpha and beta are scalars, A is a symmetric matrix and B and
C are m by n matrices.
Parameters
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether the symmetric matrix A
appears on the left or right in the operation as follows:
SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the symmetric matrix A is to be
referenced as follows:
UPLO = 'U' or 'u' Only the upper triangular part of the
symmetric matrix is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of the
symmetric matrix is to be referenced.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix C.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix C.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
m when SIDE = 'L' or 'l' and is n otherwise.
Before entry with SIDE = 'L' or 'l', the m by m part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading m by m upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading m by m lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
Before entry with SIDE = 'R' or 'r', the n by n part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading n by n upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading n by n lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, n ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n updated
matrix.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Unchanged on exit.
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Set NROWA as the number of rows of A.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
/* Function Body */
if (lsame_(side, "L")) {
nrowa = *m;
} else {
nrowa = *n;
}
upper = lsame_(uplo, "U");
/* Test the input parameters. */
info = 0;
if (! lsame_(side, "L") && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (*m < 0) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldb < max(1,*m)) {
info = 9;
} else if (*ldc < max(1,*m)) {
info = 12;
}
if (info != 0) {
xerbla_("DSYMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L30: */
}
/* L40: */
}
}
return 0;
}
/* Start the operations. */
if (lsame_(side, "L")) {
/* Form C := alpha*A*B + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp1 = *alpha * b_ref(i__, j);
temp2 = 0.;
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
c___ref(k, j) = c___ref(k, j) + temp1 * a_ref(k, i__);
temp2 += b_ref(k, j) * a_ref(k, i__);
/* L50: */
}
if (*beta == 0.) {
c___ref(i__, j) = temp1 * a_ref(i__, i__) + *alpha *
temp2;
} else {
c___ref(i__, j) = *beta * c___ref(i__, j) + temp1 *
a_ref(i__, i__) + *alpha * temp2;
}
/* L60: */
}
/* L70: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp1 = *alpha * b_ref(i__, j);
temp2 = 0.;
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
c___ref(k, j) = c___ref(k, j) + temp1 * a_ref(k, i__);
temp2 += b_ref(k, j) * a_ref(k, i__);
/* L80: */
}
if (*beta == 0.) {
c___ref(i__, j) = temp1 * a_ref(i__, i__) + *alpha *
temp2;
} else {
c___ref(i__, j) = *beta * c___ref(i__, j) + temp1 *
a_ref(i__, i__) + *alpha * temp2;
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form C := alpha*B*A + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * a_ref(j, j);
if (*beta == 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = temp1 * b_ref(i__, j);
/* L110: */
}
} else {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j) + temp1 * b_ref(
i__, j);
/* L120: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (upper) {
temp1 = *alpha * a_ref(k, j);
} else {
temp1 = *alpha * a_ref(j, k);
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c___ref(i__, j) = c___ref(i__, j) + temp1 * b_ref(i__, k);
/* L130: */
}
/* L140: */
}
i__2 = *n;
for (k = j + 1; k <= i__2; ++k) {
if (upper) {
temp1 = *alpha * a_ref(j, k);
} else {
temp1 = *alpha * a_ref(k, j);
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c___ref(i__, j) = c___ref(i__, j) + temp1 * b_ref(i__, k);
/* L150: */
}
/* L160: */
}
/* L170: */
}
}
return 0;
/* End of DSYMM . */
} /* dsymm_ */
#undef c___ref
#undef b_ref
#undef a_ref
#ifdef _cpluscplus
}
#endif

256
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dsymv_(char *uplo, integer *n, doublereal *alpha,
doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal
*beta, doublereal *y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp1, temp2;
static integer i__, j;
extern logical lsame_(char *, char *);
static integer ix, iy, jx, jy, kx, ky;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DSYMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric matrix.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y. On exit, Y is overwritten by the updated
vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*lda < max(1,*n)) {
info = 5;
} else if (*incx == 0) {
info = 7;
} else if (*incy == 0) {
info = 10;
}
if (info != 0) {
xerbla_("DSYMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0. && *beta == 1.) {
return 0;
}
/* Set up the start points in X and Y. */
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A.
First form y := beta*y. */
if (*beta != 1.) {
if (*incy == 1) {
if (*beta == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.;
/* L10: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.) {
return 0;
}
if (lsame_(uplo, "U")) {
/* Form y when A is stored in upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__] += temp1 * a_ref(i__, j);
temp2 += a_ref(i__, j) * x[i__];
/* L50: */
}
y[j] = y[j] + temp1 * a_ref(j, j) + *alpha * temp2;
/* L60: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.;
ix = kx;
iy = ky;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
y[iy] += temp1 * a_ref(i__, j);
temp2 += a_ref(i__, j) * x[ix];
ix += *incx;
iy += *incy;
/* L70: */
}
y[jy] = y[jy] + temp1 * a_ref(j, j) + *alpha * temp2;
jx += *incx;
jy += *incy;
/* L80: */
}
}
} else {
/* Form y when A is stored in lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.;
y[j] += temp1 * a_ref(j, j);
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
y[i__] += temp1 * a_ref(i__, j);
temp2 += a_ref(i__, j) * x[i__];
/* L90: */
}
y[j] += *alpha * temp2;
/* L100: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.;
y[jy] += temp1 * a_ref(j, j);
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
iy += *incy;
y[iy] += temp1 * a_ref(i__, j);
temp2 += a_ref(i__, j) * x[ix];
/* L110: */
}
y[jy] += *alpha * temp2;
jx += *incx;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of DSYMV . */
} /* dsymv_ */
#undef a_ref
#ifdef _cpluscplus
}
#endif

185
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dsyr_(char *uplo, integer *n, doublereal *alpha,
doublereal *x, integer *incx, doublereal *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j;
extern logical lsame_(char *, char *);
static integer ix, jx, kx;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DSYR performs the symmetric rank 1 operation
A := alpha*x*x' + A,
where alpha is a real scalar, x is an n element vector and A is an
n by n symmetric matrix.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced. On exit, the
upper triangular part of the array A is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced. On exit, the
lower triangular part of the array A is overwritten by the
lower triangular part of the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
--x;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*lda < max(1,*n)) {
info = 7;
}
if (info != 0) {
xerbla_("DSYR ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0.) {
return 0;
}
/* Set the start point in X if the increment is not unity. */
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A. */
if (lsame_(uplo, "U")) {
/* Form A when A is stored in upper triangle. */
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
temp = *alpha * x[j];
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[i__] * temp;
/* L10: */
}
}
/* L20: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
ix = kx;
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[ix] * temp;
ix += *incx;
/* L30: */
}
}
jx += *incx;
/* L40: */
}
}
} else {
/* Form A when A is stored in lower triangle. */
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
temp = *alpha * x[j];
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[i__] * temp;
/* L50: */
}
}
/* L60: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
ix = jx;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[ix] * temp;
ix += *incx;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
}
return 0;
/* End of DSYR . */
} /* dsyr_ */
#undef a_ref
#ifdef _cpluscplus
}
#endif

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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dsyr2_(char *uplo, integer *n, doublereal *alpha,
doublereal *x, integer *incx, doublereal *y, integer *incy,
doublereal *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp1, temp2;
static integer i__, j;
extern logical lsame_(char *, char *);
static integer ix, iy, jx, jy, kx, ky;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DSYR2 performs the symmetric rank 2 operation
A := alpha*x*y' + alpha*y*x' + A,
where alpha is a scalar, x and y are n element vectors and A is an n
by n symmetric matrix.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced. On exit, the
upper triangular part of the array A is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced. On exit, the
lower triangular part of the array A is overwritten by the
lower triangular part of the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*n)) {
info = 9;
}
if (info != 0) {
xerbla_("DSYR2 ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0.) {
return 0;
}
/* Set up the start points in X and Y if the increments are not both
unity. */
if (*incx != 1 || *incy != 1) {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
jx = kx;
jy = ky;
}
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A. */
if (lsame_(uplo, "U")) {
/* Form A when A is stored in the upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0. || y[j] != 0.) {
temp1 = *alpha * y[j];
temp2 = *alpha * x[j];
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[i__] * temp1 + y[
i__] * temp2;
/* L10: */
}
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0. || y[jy] != 0.) {
temp1 = *alpha * y[jy];
temp2 = *alpha * x[jx];
ix = kx;
iy = ky;
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[ix] * temp1 + y[iy]
* temp2;
ix += *incx;
iy += *incy;
/* L30: */
}
}
jx += *incx;
jy += *incy;
/* L40: */
}
}
} else {
/* Form A when A is stored in the lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0. || y[j] != 0.) {
temp1 = *alpha * y[j];
temp2 = *alpha * x[j];
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[i__] * temp1 + y[
i__] * temp2;
/* L50: */
}
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0. || y[jy] != 0.) {
temp1 = *alpha * y[jy];
temp2 = *alpha * x[jx];
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j) + x[ix] * temp1 + y[iy]
* temp2;
ix += *incx;
iy += *incy;
/* L70: */
}
}
jx += *incx;
jy += *incy;
/* L80: */
}
}
}
return 0;
/* End of DSYR2 . */
} /* dsyr2_ */
#undef a_ref
#ifdef _cpluscplus
}
#endif
#ifdef _cpluscplus
}
#endif

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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dsyr2k_(char *uplo, char *trans, integer *n, integer *k,
doublereal *alpha, doublereal *a, integer *lda, doublereal *b,
integer *ldb, doublereal *beta, doublereal *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer info;
static doublereal temp1, temp2;
static integer i__, j, l;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define c___ref(a_1,a_2) c__[(a_2)*c_dim1 + a_1]
/* Purpose
=======
DSYR2K performs one of the symmetric rank 2k operations
C := alpha*A*B' + alpha*B*A' + beta*C,
or
C := alpha*A'*B + alpha*B'*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A and B are n by k matrices in the first case and k by n
matrices in the second case.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
beta*C.
TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
beta*C.
TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*A +
beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrices A and B, and on entry with
TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
of rows of the matrices A and B. K must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array B must contain the matrix B, otherwise
the leading k by n part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDB must be at least max( 1, n ), otherwise LDB must
be at least max( 1, k ).
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldb < max(1,nrowa)) {
info = 9;
} else if (*ldc < max(1,*n)) {
info = 12;
}
if (info != 0) {
xerbla_("DSYR2K", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
if (upper) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L30: */
}
/* L40: */
}
}
} else {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/* Form C := alpha*A*B' + alpha*B*A' + C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L90: */
}
} else if (*beta != 1.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L100: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a_ref(j, l) != 0. || b_ref(j, l) != 0.) {
temp1 = *alpha * b_ref(j, l);
temp2 = *alpha * a_ref(j, l);
i__3 = j;
for (i__ = 1; i__ <= i__3; ++i__) {
c___ref(i__, j) = c___ref(i__, j) + a_ref(i__, l)
* temp1 + b_ref(i__, l) * temp2;
/* L110: */
}
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L140: */
}
} else if (*beta != 1.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L150: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a_ref(j, l) != 0. || b_ref(j, l) != 0.) {
temp1 = *alpha * b_ref(j, l);
temp2 = *alpha * a_ref(j, l);
i__3 = *n;
for (i__ = j; i__ <= i__3; ++i__) {
c___ref(i__, j) = c___ref(i__, j) + a_ref(i__, l)
* temp1 + b_ref(i__, l) * temp2;
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
}
} else {
/* Form C := alpha*A'*B + alpha*B'*A + C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
temp1 = 0.;
temp2 = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp1 += a_ref(l, i__) * b_ref(l, j);
temp2 += b_ref(l, i__) * a_ref(l, j);
/* L190: */
}
if (*beta == 0.) {
c___ref(i__, j) = *alpha * temp1 + *alpha * temp2;
} else {
c___ref(i__, j) = *beta * c___ref(i__, j) + *alpha *
temp1 + *alpha * temp2;
}
/* L200: */
}
/* L210: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
temp1 = 0.;
temp2 = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp1 += a_ref(l, i__) * b_ref(l, j);
temp2 += b_ref(l, i__) * a_ref(l, j);
/* L220: */
}
if (*beta == 0.) {
c___ref(i__, j) = *alpha * temp1 + *alpha * temp2;
} else {
c___ref(i__, j) = *beta * c___ref(i__, j) + *alpha *
temp1 + *alpha * temp2;
}
/* L230: */
}
/* L240: */
}
}
}
return 0;
/* End of DSYR2K. */
} /* dsyr2k_ */
#undef c___ref
#undef b_ref
#undef a_ref
#ifdef _cpluscplus
}
#endif

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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dsyrk_(char *uplo, char *trans, integer *n, integer *k,
doublereal *alpha, doublereal *a, integer *lda, doublereal *beta,
doublereal *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j, l;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define c___ref(a_1,a_2) c__[(a_2)*c_dim1 + a_1]
/* Purpose
=======
DSYRK performs one of the symmetric rank k operations
C := alpha*A*A' + beta*C,
or
C := alpha*A'*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A is an n by k matrix in the first case and a k by n matrix
in the second case.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*A' + beta*C.
TRANS = 'T' or 't' C := alpha*A'*A + beta*C.
TRANS = 'C' or 'c' C := alpha*A'*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrix A, and on entry with
TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
of rows of the matrix A. K must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldc < max(1,*n)) {
info = 10;
}
if (info != 0) {
xerbla_("DSYRK ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
if (upper) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L30: */
}
/* L40: */
}
}
} else {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/* Form C := alpha*A*A' + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L90: */
}
} else if (*beta != 1.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L100: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a_ref(j, l) != 0.) {
temp = *alpha * a_ref(j, l);
i__3 = j;
for (i__ = 1; i__ <= i__3; ++i__) {
c___ref(i__, j) = c___ref(i__, j) + temp * a_ref(
i__, l);
/* L110: */
}
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c___ref(i__, j) = 0.;
/* L140: */
}
} else if (*beta != 1.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c___ref(i__, j) = *beta * c___ref(i__, j);
/* L150: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a_ref(j, l) != 0.) {
temp = *alpha * a_ref(j, l);
i__3 = *n;
for (i__ = j; i__ <= i__3; ++i__) {
c___ref(i__, j) = c___ref(i__, j) + temp * a_ref(
i__, l);
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
}
} else {
/* Form C := alpha*A'*A + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a_ref(l, i__) * a_ref(l, j);
/* L190: */
}
if (*beta == 0.) {
c___ref(i__, j) = *alpha * temp;
} else {
c___ref(i__, j) = *alpha * temp + *beta * c___ref(i__,
j);
}
/* L200: */
}
/* L210: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
temp = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a_ref(l, i__) * a_ref(l, j);
/* L220: */
}
if (*beta == 0.) {
c___ref(i__, j) = *alpha * temp;
} else {
c___ref(i__, j) = *alpha * temp + *beta * c___ref(i__,
j);
}
/* L230: */
}
/* L240: */
}
}
}
return 0;
/* End of DSYRK . */
} /* dsyrk_ */
#undef c___ref
#undef a_ref
#ifdef _cpluscplus
}
#endif

354
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dtbmv_(char *uplo, char *trans, char *diag, integer *n,
integer *k, doublereal *a, integer *lda, doublereal *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j, l;
extern logical lsame_(char *, char *);
static integer kplus1, ix, jx, kx;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DTBMV performs one of the matrix-vector operations
x := A*x, or x := A'*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular band matrix, with ( k + 1 ) diagonals.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A'*x.
TRANS = 'C' or 'c' x := A'*x.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
K - INTEGER.
On entry with UPLO = 'U' or 'u', K specifies the number of
super-diagonals of the matrix A.
On entry with UPLO = 'L' or 'l', K specifies the number of
sub-diagonals of the matrix A.
K must satisfy 0 .le. K.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
by n part of the array A must contain the upper triangular
band part of the matrix of coefficients, supplied column by
column, with the leading diagonal of the matrix in row
( k + 1 ) of the array, the first super-diagonal starting at
position 2 in row k, and so on. The top left k by k triangle
of the array A is not referenced.
The following program segment will transfer an upper
triangular band matrix from conventional full matrix storage
to band storage:
DO 20, J = 1, N
M = K + 1 - J
DO 10, I = MAX( 1, J - K ), J
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
by n part of the array A must contain the lower triangular
band part of the matrix of coefficients, supplied column by
column, with the leading diagonal of the matrix in row 1 of
the array, the first sub-diagonal starting at position 1 in
row 2, and so on. The bottom right k by k triangle of the
array A is not referenced.
The following program segment will transfer a lower
triangular band matrix from conventional full matrix storage
to band storage:
DO 20, J = 1, N
M = 1 - J
DO 10, I = J, MIN( N, J + K )
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Note that when DIAG = 'U' or 'u' the elements of the array A
corresponding to the diagonal elements of the matrix are not
referenced, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
( k + 1 ).
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
tranformed vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*k < 0) {
info = 5;
} else if (*lda < *k + 1) {
info = 7;
} else if (*incx == 0) {
info = 9;
}
if (info != 0) {
xerbla_("DTBMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
nounit = lsame_(diag, "N");
/* Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops. */
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through A. */
if (lsame_(trans, "N")) {
/* Form x := A*x. */
if (lsame_(uplo, "U")) {
kplus1 = *k + 1;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
temp = x[j];
l = kplus1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__4 = j - 1;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
x[i__] += temp * a_ref(l + i__, j);
/* L10: */
}
if (nounit) {
x[j] *= a_ref(kplus1, j);
}
}
/* L20: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = x[jx];
ix = kx;
l = kplus1 - j;
/* Computing MAX */
i__4 = 1, i__2 = j - *k;
i__3 = j - 1;
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
x[ix] += temp * a_ref(l + i__, j);
ix += *incx;
/* L30: */
}
if (nounit) {
x[jx] *= a_ref(kplus1, j);
}
}
jx += *incx;
if (j > *k) {
kx += *incx;
}
/* L40: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
if (x[j] != 0.) {
temp = x[j];
l = 1 - j;
/* Computing MIN */
i__1 = *n, i__3 = j + *k;
i__4 = j + 1;
for (i__ = min(i__1,i__3); i__ >= i__4; --i__) {
x[i__] += temp * a_ref(l + i__, j);
/* L50: */
}
if (nounit) {
x[j] *= a_ref(1, j);
}
}
/* L60: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
if (x[jx] != 0.) {
temp = x[jx];
ix = kx;
l = 1 - j;
/* Computing MIN */
i__4 = *n, i__1 = j + *k;
i__3 = j + 1;
for (i__ = min(i__4,i__1); i__ >= i__3; --i__) {
x[ix] += temp * a_ref(l + i__, j);
ix -= *incx;
/* L70: */
}
if (nounit) {
x[jx] *= a_ref(1, j);
}
}
jx -= *incx;
if (*n - j >= *k) {
kx -= *incx;
}
/* L80: */
}
}
}
} else {
/* Form x := A'*x. */
if (lsame_(uplo, "U")) {
kplus1 = *k + 1;
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
temp = x[j];
l = kplus1 - j;
if (nounit) {
temp *= a_ref(kplus1, j);
}
/* Computing MAX */
i__4 = 1, i__1 = j - *k;
i__3 = max(i__4,i__1);
for (i__ = j - 1; i__ >= i__3; --i__) {
temp += a_ref(l + i__, j) * x[i__];
/* L90: */
}
x[j] = temp;
/* L100: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
temp = x[jx];
kx -= *incx;
ix = kx;
l = kplus1 - j;
if (nounit) {
temp *= a_ref(kplus1, j);
}
/* Computing MAX */
i__4 = 1, i__1 = j - *k;
i__3 = max(i__4,i__1);
for (i__ = j - 1; i__ >= i__3; --i__) {
temp += a_ref(l + i__, j) * x[ix];
ix -= *incx;
/* L110: */
}
x[jx] = temp;
jx -= *incx;
/* L120: */
}
}
} else {
if (*incx == 1) {
i__3 = *n;
for (j = 1; j <= i__3; ++j) {
temp = x[j];
l = 1 - j;
if (nounit) {
temp *= a_ref(1, j);
}
/* Computing MIN */
i__1 = *n, i__2 = j + *k;
i__4 = min(i__1,i__2);
for (i__ = j + 1; i__ <= i__4; ++i__) {
temp += a_ref(l + i__, j) * x[i__];
/* L130: */
}
x[j] = temp;
/* L140: */
}
} else {
jx = kx;
i__3 = *n;
for (j = 1; j <= i__3; ++j) {
temp = x[jx];
kx += *incx;
ix = kx;
l = 1 - j;
if (nounit) {
temp *= a_ref(1, j);
}
/* Computing MIN */
i__1 = *n, i__2 = j + *k;
i__4 = min(i__1,i__2);
for (i__ = j + 1; i__ <= i__4; ++i__) {
temp += a_ref(l + i__, j) * x[ix];
ix += *incx;
/* L150: */
}
x[jx] = temp;
jx += *incx;
/* L160: */
}
}
}
}
return 0;
/* End of DTBMV . */
} /* dtbmv_ */
#undef a_ref
#ifdef _cpluscplus
}
#endif

357
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dtbsv_(char *uplo, char *trans, char *diag, integer *n,
integer *k, doublereal *a, integer *lda, doublereal *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j, l;
extern logical lsame_(char *, char *);
static integer kplus1, ix, jx, kx;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DTBSV solves one of the systems of equations
A*x = b, or A'*x = b,
where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular band matrix, with ( k + 1 )
diagonals.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the equations to be solved as
follows:
TRANS = 'N' or 'n' A*x = b.
TRANS = 'T' or 't' A'*x = b.
TRANS = 'C' or 'c' A'*x = b.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
K - INTEGER.
On entry with UPLO = 'U' or 'u', K specifies the number of
super-diagonals of the matrix A.
On entry with UPLO = 'L' or 'l', K specifies the number of
sub-diagonals of the matrix A.
K must satisfy 0 .le. K.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
by n part of the array A must contain the upper triangular
band part of the matrix of coefficients, supplied column by
column, with the leading diagonal of the matrix in row
( k + 1 ) of the array, the first super-diagonal starting at
position 2 in row k, and so on. The top left k by k triangle
of the array A is not referenced.
The following program segment will transfer an upper
triangular band matrix from conventional full matrix storage
to band storage:
DO 20, J = 1, N
M = K + 1 - J
DO 10, I = MAX( 1, J - K ), J
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
by n part of the array A must contain the lower triangular
band part of the matrix of coefficients, supplied column by
column, with the leading diagonal of the matrix in row 1 of
the array, the first sub-diagonal starting at position 1 in
row 2, and so on. The bottom right k by k triangle of the
array A is not referenced.
The following program segment will transfer a lower
triangular band matrix from conventional full matrix storage
to band storage:
DO 20, J = 1, N
M = 1 - J
DO 10, I = J, MIN( N, J + K )
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Note that when DIAG = 'U' or 'u' the elements of the array A
corresponding to the diagonal elements of the matrix are not
referenced, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
( k + 1 ).
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*k < 0) {
info = 5;
} else if (*lda < *k + 1) {
info = 7;
} else if (*incx == 0) {
info = 9;
}
if (info != 0) {
xerbla_("DTBSV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
nounit = lsame_(diag, "N");
/* Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops. */
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/* Start the operations. In this version the elements of A are
accessed by sequentially with one pass through A. */
if (lsame_(trans, "N")) {
/* Form x := inv( A )*x. */
if (lsame_(uplo, "U")) {
kplus1 = *k + 1;
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
if (x[j] != 0.) {
l = kplus1 - j;
if (nounit) {
x[j] /= a_ref(kplus1, j);
}
temp = x[j];
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__1 = max(i__2,i__3);
for (i__ = j - 1; i__ >= i__1; --i__) {
x[i__] -= temp * a_ref(l + i__, j);
/* L10: */
}
}
/* L20: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
kx -= *incx;
if (x[jx] != 0.) {
ix = kx;
l = kplus1 - j;
if (nounit) {
x[jx] /= a_ref(kplus1, j);
}
temp = x[jx];
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__1 = max(i__2,i__3);
for (i__ = j - 1; i__ >= i__1; --i__) {
x[ix] -= temp * a_ref(l + i__, j);
ix -= *incx;
/* L30: */
}
}
jx -= *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
l = 1 - j;
if (nounit) {
x[j] /= a_ref(1, j);
}
temp = x[j];
/* Computing MIN */
i__3 = *n, i__4 = j + *k;
i__2 = min(i__3,i__4);
for (i__ = j + 1; i__ <= i__2; ++i__) {
x[i__] -= temp * a_ref(l + i__, j);
/* L50: */
}
}
/* L60: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
kx += *incx;
if (x[jx] != 0.) {
ix = kx;
l = 1 - j;
if (nounit) {
x[jx] /= a_ref(1, j);
}
temp = x[jx];
/* Computing MIN */
i__3 = *n, i__4 = j + *k;
i__2 = min(i__3,i__4);
for (i__ = j + 1; i__ <= i__2; ++i__) {
x[ix] -= temp * a_ref(l + i__, j);
ix += *incx;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
}
} else {
/* Form x := inv( A')*x. */
if (lsame_(uplo, "U")) {
kplus1 = *k + 1;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[j];
l = kplus1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__4 = j - 1;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
temp -= a_ref(l + i__, j) * x[i__];
/* L90: */
}
if (nounit) {
temp /= a_ref(kplus1, j);
}
x[j] = temp;
/* L100: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[jx];
ix = kx;
l = kplus1 - j;
/* Computing MAX */
i__4 = 1, i__2 = j - *k;
i__3 = j - 1;
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
temp -= a_ref(l + i__, j) * x[ix];
ix += *incx;
/* L110: */
}
if (nounit) {
temp /= a_ref(kplus1, j);
}
x[jx] = temp;
jx += *incx;
if (j > *k) {
kx += *incx;
}
/* L120: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
temp = x[j];
l = 1 - j;
/* Computing MIN */
i__1 = *n, i__3 = j + *k;
i__4 = j + 1;
for (i__ = min(i__1,i__3); i__ >= i__4; --i__) {
temp -= a_ref(l + i__, j) * x[i__];
/* L130: */
}
if (nounit) {
temp /= a_ref(1, j);
}
x[j] = temp;
/* L140: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
temp = x[jx];
ix = kx;
l = 1 - j;
/* Computing MIN */
i__4 = *n, i__1 = j + *k;
i__3 = j + 1;
for (i__ = min(i__4,i__1); i__ >= i__3; --i__) {
temp -= a_ref(l + i__, j) * x[ix];
ix -= *incx;
/* L150: */
}
if (nounit) {
temp /= a_ref(1, j);
}
x[jx] = temp;
jx -= *incx;
if (*n - j >= *k) {
kx -= *incx;
}
/* L160: */
}
}
}
}
return 0;
/* End of DTBSV . */
} /* dtbsv_ */
#undef a_ref
#ifdef _cpluscplus
}
#endif

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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dtpmv_(char *uplo, char *trans, char *diag, integer *n,
doublereal *ap, doublereal *x, integer *incx)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j, k;
extern logical lsame_(char *, char *);
static integer kk, ix, jx, kx;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
/* Purpose
=======
DTPMV performs one of the matrix-vector operations
x := A*x, or x := A'*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix, supplied in packed form.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A'*x.
TRANS = 'C' or 'c' x := A'*x.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
AP - DOUBLE PRECISION array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = 'U' or 'u', the array AP must
contain the upper triangular matrix packed sequentially,
column by column, so that AP( 1 ) contains a( 1, 1 ),
AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
respectively, and so on.
Before entry with UPLO = 'L' or 'l', the array AP must
contain the lower triangular matrix packed sequentially,
column by column, so that AP( 1 ) contains a( 1, 1 ),
AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
respectively, and so on.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced, but are assumed to be unity.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
tranformed vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
--x;
--ap;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*incx == 0) {
info = 7;
}
if (info != 0) {
xerbla_("DTPMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
nounit = lsame_(diag, "N");
/* Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops. */
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/* Start the operations. In this version the elements of AP are
accessed sequentially with one pass through AP. */
if (lsame_(trans, "N")) {
/* Form x:= A*x. */
if (lsame_(uplo, "U")) {
kk = 1;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
temp = x[j];
k = kk;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__] += temp * ap[k];
++k;
/* L10: */
}
if (nounit) {
x[j] *= ap[kk + j - 1];
}
}
kk += j;
/* L20: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = x[jx];
ix = kx;
i__2 = kk + j - 2;
for (k = kk; k <= i__2; ++k) {
x[ix] += temp * ap[k];
ix += *incx;
/* L30: */
}
if (nounit) {
x[jx] *= ap[kk + j - 1];
}
}
jx += *incx;
kk += j;
/* L40: */
}
}
} else {
kk = *n * (*n + 1) / 2;
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
if (x[j] != 0.) {
temp = x[j];
k = kk;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
x[i__] += temp * ap[k];
--k;
/* L50: */
}
if (nounit) {
x[j] *= ap[kk - *n + j];
}
}
kk -= *n - j + 1;
/* L60: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
if (x[jx] != 0.) {
temp = x[jx];
ix = kx;
i__1 = kk - (*n - (j + 1));
for (k = kk; k >= i__1; --k) {
x[ix] += temp * ap[k];
ix -= *incx;
/* L70: */
}
if (nounit) {
x[jx] *= ap[kk - *n + j];
}
}
jx -= *incx;
kk -= *n - j + 1;
/* L80: */
}
}
}
} else {
/* Form x := A'*x. */
if (lsame_(uplo, "U")) {
kk = *n * (*n + 1) / 2;
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
temp = x[j];
if (nounit) {
temp *= ap[kk];
}
k = kk - 1;
for (i__ = j - 1; i__ >= 1; --i__) {
temp += ap[k] * x[i__];
--k;
/* L90: */
}
x[j] = temp;
kk -= j;
/* L100: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
temp = x[jx];
ix = jx;
if (nounit) {
temp *= ap[kk];
}
i__1 = kk - j + 1;
for (k = kk - 1; k >= i__1; --k) {
ix -= *incx;
temp += ap[k] * x[ix];
/* L110: */
}
x[jx] = temp;
jx -= *incx;
kk -= j;
/* L120: */
}
}
} else {
kk = 1;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[j];
if (nounit) {
temp *= ap[kk];
}
k = kk + 1;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
temp += ap[k] * x[i__];
++k;
/* L130: */
}
x[j] = temp;
kk += *n - j + 1;
/* L140: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[jx];
ix = jx;
if (nounit) {
temp *= ap[kk];
}
i__2 = kk + *n - j;
for (k = kk + 1; k <= i__2; ++k) {
ix += *incx;
temp += ap[k] * x[ix];
/* L150: */
}
x[jx] = temp;
jx += *incx;
kk += *n - j + 1;
/* L160: */
}
}
}
}
return 0;
/* End of DTPMV . */
} /* dtpmv_ */
#ifdef _cpluscplus
}
#endif

298
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dtpsv_(char *uplo, char *trans, char *diag, integer *n,
doublereal *ap, doublereal *x, integer *incx)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j, k;
extern logical lsame_(char *, char *);
static integer kk, ix, jx, kx;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
/* Purpose
=======
DTPSV solves one of the systems of equations
A*x = b, or A'*x = b,
where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix, supplied in packed form.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the equations to be solved as
follows:
TRANS = 'N' or 'n' A*x = b.
TRANS = 'T' or 't' A'*x = b.
TRANS = 'C' or 'c' A'*x = b.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
AP - DOUBLE PRECISION array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = 'U' or 'u', the array AP must
contain the upper triangular matrix packed sequentially,
column by column, so that AP( 1 ) contains a( 1, 1 ),
AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
respectively, and so on.
Before entry with UPLO = 'L' or 'l', the array AP must
contain the lower triangular matrix packed sequentially,
column by column, so that AP( 1 ) contains a( 1, 1 ),
AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
respectively, and so on.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced, but are assumed to be unity.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
--x;
--ap;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*incx == 0) {
info = 7;
}
if (info != 0) {
xerbla_("DTPSV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
nounit = lsame_(diag, "N");
/* Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops. */
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/* Start the operations. In this version the elements of AP are
accessed sequentially with one pass through AP. */
if (lsame_(trans, "N")) {
/* Form x := inv( A )*x. */
if (lsame_(uplo, "U")) {
kk = *n * (*n + 1) / 2;
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
if (x[j] != 0.) {
if (nounit) {
x[j] /= ap[kk];
}
temp = x[j];
k = kk - 1;
for (i__ = j - 1; i__ >= 1; --i__) {
x[i__] -= temp * ap[k];
--k;
/* L10: */
}
}
kk -= j;
/* L20: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
if (x[jx] != 0.) {
if (nounit) {
x[jx] /= ap[kk];
}
temp = x[jx];
ix = jx;
i__1 = kk - j + 1;
for (k = kk - 1; k >= i__1; --k) {
ix -= *incx;
x[ix] -= temp * ap[k];
/* L30: */
}
}
jx -= *incx;
kk -= j;
/* L40: */
}
}
} else {
kk = 1;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
if (nounit) {
x[j] /= ap[kk];
}
temp = x[j];
k = kk + 1;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
x[i__] -= temp * ap[k];
++k;
/* L50: */
}
}
kk += *n - j + 1;
/* L60: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
if (nounit) {
x[jx] /= ap[kk];
}
temp = x[jx];
ix = jx;
i__2 = kk + *n - j;
for (k = kk + 1; k <= i__2; ++k) {
ix += *incx;
x[ix] -= temp * ap[k];
/* L70: */
}
}
jx += *incx;
kk += *n - j + 1;
/* L80: */
}
}
}
} else {
/* Form x := inv( A' )*x. */
if (lsame_(uplo, "U")) {
kk = 1;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[j];
k = kk;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
temp -= ap[k] * x[i__];
++k;
/* L90: */
}
if (nounit) {
temp /= ap[kk + j - 1];
}
x[j] = temp;
kk += j;
/* L100: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[jx];
ix = kx;
i__2 = kk + j - 2;
for (k = kk; k <= i__2; ++k) {
temp -= ap[k] * x[ix];
ix += *incx;
/* L110: */
}
if (nounit) {
temp /= ap[kk + j - 1];
}
x[jx] = temp;
jx += *incx;
kk += j;
/* L120: */
}
}
} else {
kk = *n * (*n + 1) / 2;
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
temp = x[j];
k = kk;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
temp -= ap[k] * x[i__];
--k;
/* L130: */
}
if (nounit) {
temp /= ap[kk - *n + j];
}
x[j] = temp;
kk -= *n - j + 1;
/* L140: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
temp = x[jx];
ix = kx;
i__1 = kk - (*n - (j + 1));
for (k = kk; k >= i__1; --k) {
temp -= ap[k] * x[ix];
ix -= *incx;
/* L150: */
}
if (nounit) {
temp /= ap[kk - *n + j];
}
x[jx] = temp;
jx -= *incx;
kk -= *n - j + 1;
/* L160: */
}
}
}
}
return 0;
/* End of DTPSV . */
} /* dtpsv_ */
#ifdef _cpluscplus
}
#endif

381
ext/f2c_blas/dtrmm.c Normal file
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
lda, doublereal *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j, k;
static logical lside;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
/* Purpose
=======
DTRMM performs one of the matrix-matrix operations
B := alpha*op( A )*B, or B := alpha*B*op( A ),
where alpha is a scalar, B is an m by n matrix, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A'.
Parameters
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) multiplies B from
the left or right as follows:
SIDE = 'L' or 'l' B := alpha*op( A )*B.
SIDE = 'R' or 'r' B := alpha*B*op( A ).
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = A'.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the matrix B, and on exit is overwritten by the
transformed matrix.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("DTRMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = 0.;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*A*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
if (b_ref(k, j) != 0.) {
temp = *alpha * b_ref(k, j);
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
b_ref(i__, j) = b_ref(i__, j) + temp * a_ref(
i__, k);
/* L30: */
}
if (nounit) {
temp *= a_ref(k, k);
}
b_ref(k, j) = temp;
}
/* L40: */
}
/* L50: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (k = *m; k >= 1; --k) {
if (b_ref(k, j) != 0.) {
temp = *alpha * b_ref(k, j);
b_ref(k, j) = temp;
if (nounit) {
b_ref(k, j) = b_ref(k, j) * a_ref(k, k);
}
i__2 = *m;
for (i__ = k + 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = b_ref(i__, j) + temp * a_ref(
i__, k);
/* L60: */
}
}
/* L70: */
}
/* L80: */
}
}
} else {
/* Form B := alpha*A'*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp = b_ref(i__, j);
if (nounit) {
temp *= a_ref(i__, i__);
}
i__2 = i__ - 1;
for (k = 1; k <= i__2; ++k) {
temp += a_ref(k, i__) * b_ref(k, j);
/* L90: */
}
b_ref(i__, j) = *alpha * temp;
/* L100: */
}
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = b_ref(i__, j);
if (nounit) {
temp *= a_ref(i__, i__);
}
i__3 = *m;
for (k = i__ + 1; k <= i__3; ++k) {
temp += a_ref(k, i__) * b_ref(k, j);
/* L120: */
}
b_ref(i__, j) = *alpha * temp;
/* L130: */
}
/* L140: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*A. */
if (upper) {
for (j = *n; j >= 1; --j) {
temp = *alpha;
if (nounit) {
temp *= a_ref(j, j);
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, j) = temp * b_ref(i__, j);
/* L150: */
}
i__1 = j - 1;
for (k = 1; k <= i__1; ++k) {
if (a_ref(k, j) != 0.) {
temp = *alpha * a_ref(k, j);
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = b_ref(i__, j) + temp * b_ref(
i__, k);
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = *alpha;
if (nounit) {
temp *= a_ref(j, j);
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = temp * b_ref(i__, j);
/* L190: */
}
i__2 = *n;
for (k = j + 1; k <= i__2; ++k) {
if (a_ref(k, j) != 0.) {
temp = *alpha * a_ref(k, j);
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b_ref(i__, j) = b_ref(i__, j) + temp * b_ref(
i__, k);
/* L200: */
}
}
/* L210: */
}
/* L220: */
}
}
} else {
/* Form B := alpha*B*A'. */
if (upper) {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
i__2 = k - 1;
for (j = 1; j <= i__2; ++j) {
if (a_ref(j, k) != 0.) {
temp = *alpha * a_ref(j, k);
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b_ref(i__, j) = b_ref(i__, j) + temp * b_ref(
i__, k);
/* L230: */
}
}
/* L240: */
}
temp = *alpha;
if (nounit) {
temp *= a_ref(k, k);
}
if (temp != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, k) = temp * b_ref(i__, k);
/* L250: */
}
}
/* L260: */
}
} else {
for (k = *n; k >= 1; --k) {
i__1 = *n;
for (j = k + 1; j <= i__1; ++j) {
if (a_ref(j, k) != 0.) {
temp = *alpha * a_ref(j, k);
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = b_ref(i__, j) + temp * b_ref(
i__, k);
/* L270: */
}
}
/* L280: */
}
temp = *alpha;
if (nounit) {
temp *= a_ref(k, k);
}
if (temp != 1.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, k) = temp * b_ref(i__, k);
/* L290: */
}
}
/* L300: */
}
}
}
}
return 0;
/* End of DTRMM . */
} /* dtrmm_ */
#undef b_ref
#undef a_ref
#ifdef _cpluscplus
}
#endif

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ext/f2c_blas/dtrmv.c Normal file
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n,
doublereal *a, integer *lda, doublereal *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j;
extern logical lsame_(char *, char *);
static integer ix, jx, kx;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DTRMV performs one of the matrix-vector operations
x := A*x, or x := A'*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A'*x.
TRANS = 'C' or 'c' x := A'*x.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
tranformed vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,*n)) {
info = 6;
} else if (*incx == 0) {
info = 8;
}
if (info != 0) {
xerbla_("DTRMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
nounit = lsame_(diag, "N");
/* Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops. */
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through A. */
if (lsame_(trans, "N")) {
/* Form x := A*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
temp = x[j];
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__] += temp * a_ref(i__, j);
/* L10: */
}
if (nounit) {
x[j] *= a_ref(j, j);
}
}
/* L20: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = x[jx];
ix = kx;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
x[ix] += temp * a_ref(i__, j);
ix += *incx;
/* L30: */
}
if (nounit) {
x[jx] *= a_ref(j, j);
}
}
jx += *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
if (x[j] != 0.) {
temp = x[j];
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
x[i__] += temp * a_ref(i__, j);
/* L50: */
}
if (nounit) {
x[j] *= a_ref(j, j);
}
}
/* L60: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
if (x[jx] != 0.) {
temp = x[jx];
ix = kx;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
x[ix] += temp * a_ref(i__, j);
ix -= *incx;
/* L70: */
}
if (nounit) {
x[jx] *= a_ref(j, j);
}
}
jx -= *incx;
/* L80: */
}
}
}
} else {
/* Form x := A'*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
temp = x[j];
if (nounit) {
temp *= a_ref(j, j);
}
for (i__ = j - 1; i__ >= 1; --i__) {
temp += a_ref(i__, j) * x[i__];
/* L90: */
}
x[j] = temp;
/* L100: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
temp = x[jx];
ix = jx;
if (nounit) {
temp *= a_ref(j, j);
}
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
temp += a_ref(i__, j) * x[ix];
/* L110: */
}
x[jx] = temp;
jx -= *incx;
/* L120: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[j];
if (nounit) {
temp *= a_ref(j, j);
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
temp += a_ref(i__, j) * x[i__];
/* L130: */
}
x[j] = temp;
/* L140: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[jx];
ix = jx;
if (nounit) {
temp *= a_ref(j, j);
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
temp += a_ref(i__, j) * x[ix];
/* L150: */
}
x[jx] = temp;
jx += *incx;
/* L160: */
}
}
}
}
return 0;
/* End of DTRMV . */
} /* dtrmv_ */
#undef a_ref
#ifdef _cpluscplus
}
#endif

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ext/f2c_blas/dtrsm.c Normal file
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
lda, doublereal *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j, k;
static logical lside;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
/* Purpose
=======
DTRSM solves one of the matrix equations
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A'.
The matrix X is overwritten on B.
Parameters
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = 'L' or 'l' op( A )*X = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = A'.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B, and on exit is
overwritten by the solution matrix X.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("DTRSM ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = 0.;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*inv( A )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = *alpha * b_ref(i__, j);
/* L30: */
}
}
for (k = *m; k >= 1; --k) {
if (b_ref(k, j) != 0.) {
if (nounit) {
b_ref(k, j) = b_ref(k, j) / a_ref(k, k);
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - b_ref(k, j) *
a_ref(i__, k);
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = *alpha * b_ref(i__, j);
/* L70: */
}
}
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
if (b_ref(k, j) != 0.) {
if (nounit) {
b_ref(k, j) = b_ref(k, j) / a_ref(k, k);
}
i__3 = *m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - b_ref(k, j) *
a_ref(i__, k);
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form B := alpha*inv( A' )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = *alpha * b_ref(i__, j);
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
temp -= a_ref(k, i__) * b_ref(k, j);
/* L110: */
}
if (nounit) {
temp /= a_ref(i__, i__);
}
b_ref(i__, j) = temp;
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp = *alpha * b_ref(i__, j);
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
temp -= a_ref(k, i__) * b_ref(k, j);
/* L140: */
}
if (nounit) {
temp /= a_ref(i__, i__);
}
b_ref(i__, j) = temp;
/* L150: */
}
/* L160: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*inv( A ). */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = *alpha * b_ref(i__, j);
/* L170: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (a_ref(k, j) != 0.) {
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - a_ref(k, j) *
b_ref(i__, k);
/* L180: */
}
}
/* L190: */
}
if (nounit) {
temp = 1. / a_ref(j, j);
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = temp * b_ref(i__, j);
/* L200: */
}
}
/* L210: */
}
} else {
for (j = *n; j >= 1; --j) {
if (*alpha != 1.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, j) = *alpha * b_ref(i__, j);
/* L220: */
}
}
i__1 = *n;
for (k = j + 1; k <= i__1; ++k) {
if (a_ref(k, j) != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - a_ref(k, j) *
b_ref(i__, k);
/* L230: */
}
}
/* L240: */
}
if (nounit) {
temp = 1. / a_ref(j, j);
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, j) = temp * b_ref(i__, j);
/* L250: */
}
}
/* L260: */
}
}
} else {
/* Form B := alpha*B*inv( A' ). */
if (upper) {
for (k = *n; k >= 1; --k) {
if (nounit) {
temp = 1. / a_ref(k, k);
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, k) = temp * b_ref(i__, k);
/* L270: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
if (a_ref(j, k) != 0.) {
temp = a_ref(j, k);
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - temp * b_ref(
i__, k);
/* L280: */
}
}
/* L290: */
}
if (*alpha != 1.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, k) = *alpha * b_ref(i__, k);
/* L300: */
}
}
/* L310: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
temp = 1. / a_ref(k, k);
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, k) = temp * b_ref(i__, k);
/* L320: */
}
}
i__2 = *n;
for (j = k + 1; j <= i__2; ++j) {
if (a_ref(j, k) != 0.) {
temp = a_ref(j, k);
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - temp * b_ref(
i__, k);
/* L330: */
}
}
/* L340: */
}
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, k) = *alpha * b_ref(i__, k);
/* L350: */
}
}
/* L360: */
}
}
}
}
return 0;
/* End of DTRSM . */
} /* dtrsm_ */
#undef b_ref
#undef a_ref
#ifdef _cpluscplus
}
#endif

285
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@ -0,0 +1,285 @@
#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int dtrsv_(char *uplo, char *trans, char *diag, integer *n,
doublereal *a, integer *lda, doublereal *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer info;
static doublereal temp;
static integer i__, j;
extern logical lsame_(char *, char *);
static integer ix, jx, kx;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* Purpose
=======
DTRSV solves one of the systems of equations
A*x = b, or A'*x = b,
where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
Parameters
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the equations to be solved as
follows:
TRANS = 'N' or 'n' A*x = b.
TRANS = 'T' or 't' A'*x = b.
TRANS = 'C' or 'c' A'*x = b.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,*n)) {
info = 6;
} else if (*incx == 0) {
info = 8;
}
if (info != 0) {
xerbla_("DTRSV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
nounit = lsame_(diag, "N");
/* Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops. */
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/* Start the operations. In this version the elements of A are
accessed sequentially with one pass through A. */
if (lsame_(trans, "N")) {
/* Form x := inv( A )*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
if (x[j] != 0.) {
if (nounit) {
x[j] /= a_ref(j, j);
}
temp = x[j];
for (i__ = j - 1; i__ >= 1; --i__) {
x[i__] -= temp * a_ref(i__, j);
/* L10: */
}
}
/* L20: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
if (x[jx] != 0.) {
if (nounit) {
x[jx] /= a_ref(j, j);
}
temp = x[jx];
ix = jx;
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
x[ix] -= temp * a_ref(i__, j);
/* L30: */
}
}
jx -= *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
if (nounit) {
x[j] /= a_ref(j, j);
}
temp = x[j];
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
x[i__] -= temp * a_ref(i__, j);
/* L50: */
}
}
/* L60: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
if (nounit) {
x[jx] /= a_ref(j, j);
}
temp = x[jx];
ix = jx;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
x[ix] -= temp * a_ref(i__, j);
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
}
} else {
/* Form x := inv( A' )*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[j];
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
temp -= a_ref(i__, j) * x[i__];
/* L90: */
}
if (nounit) {
temp /= a_ref(j, j);
}
x[j] = temp;
/* L100: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[jx];
ix = kx;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
temp -= a_ref(i__, j) * x[ix];
ix += *incx;
/* L110: */
}
if (nounit) {
temp /= a_ref(j, j);
}
x[jx] = temp;
jx += *incx;
/* L120: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
temp = x[j];
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
temp -= a_ref(i__, j) * x[i__];
/* L130: */
}
if (nounit) {
temp /= a_ref(j, j);
}
x[j] = temp;
/* L140: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
temp = x[jx];
ix = kx;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
temp -= a_ref(i__, j) * x[ix];
ix -= *incx;
/* L150: */
}
if (nounit) {
temp /= a_ref(j, j);
}
x[jx] = temp;
jx -= *incx;
/* L160: */
}
}
}
}
return 0;
/* End of DTRSV . */
} /* dtrsv_ */
#undef a_ref
#ifdef _cpluscplus
}
#endif

55
ext/f2c_blas/dzasum.c Normal file
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@ -0,0 +1,55 @@
#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
doublereal dzasum_(integer *n, doublecomplex *zx, integer *incx)
{
/* System generated locals */
integer i__1;
doublereal ret_val;
/* Local variables */
static integer i__;
static doublereal stemp;
extern doublereal dcabs1_(doublecomplex *);
static integer ix;
/* takes the sum of the absolute values.
jack dongarra, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
Parameter adjustments */
--zx;
/* Function Body */
ret_val = 0.;
stemp = 0.;
if (*n <= 0 || *incx <= 0) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp += dcabs1_(&zx[ix]);
ix += *incx;
/* L10: */
}
ret_val = stemp;
return ret_val;
/* code for increment equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp += dcabs1_(&zx[i__]);
/* L30: */
}
ret_val = stemp;
return ret_val;
} /* dzasum_ */
#ifdef _cpluscplus
}
#endif

82
ext/f2c_blas/dznrm2.c Normal file
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@ -0,0 +1,82 @@
#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx)
{
/* The following loop is equivalent to this call to the LAPACK
auxiliary routine:
CALL ZLASSQ( N, X, INCX, SCALE, SSQ ) */
/* System generated locals */
integer i__1, i__2, i__3;
doublereal ret_val, d__1;
/* Builtin functions */
double d_imag(doublecomplex *), sqrt(doublereal);
/* Local variables */
static doublereal temp, norm, scale;
static integer ix;
static doublereal ssq;
/* DZNRM2 returns the euclidean norm of a vector via the function
name, so that
DZNRM2 := sqrt( conjg( x' )*x )
-- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to ZLASSQ.
Sven Hammarling, Nag Ltd.
Parameter adjustments */
--x;
/* Function Body */
if (*n < 1 || *incx < 1) {
norm = 0.;
} else {
scale = 0.;
ssq = 1.;
i__1 = (*n - 1) * *incx + 1;
i__2 = *incx;
for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
i__3 = ix;
if (x[i__3].r != 0.) {
i__3 = ix;
temp = (d__1 = x[i__3].r, abs(d__1));
if (scale < temp) {
/* Computing 2nd power */
d__1 = scale / temp;
ssq = ssq * (d__1 * d__1) + 1.;
scale = temp;
} else {
/* Computing 2nd power */
d__1 = temp / scale;
ssq += d__1 * d__1;
}
}
if (d_imag(&x[ix]) != 0.) {
temp = (d__1 = d_imag(&x[ix]), abs(d__1));
if (scale < temp) {
/* Computing 2nd power */
d__1 = scale / temp;
ssq = ssq * (d__1 * d__1) + 1.;
scale = temp;
} else {
/* Computing 2nd power */
d__1 = temp / scale;
ssq += d__1 * d__1;
}
}
/* L10: */
}
norm = scale * sqrt(ssq);
}
ret_val = norm;
return ret_val;
/* End of DZNRM2. */
} /* dznrm2_ */
#ifdef _cpluscplus
}
#endif

67
ext/f2c_blas/idamax.c Normal file
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@ -0,0 +1,67 @@
#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
integer idamax_(integer *n, doublereal *dx, integer *incx)
{
/* System generated locals */
integer ret_val, i__1;
doublereal d__1;
/* Local variables */
static doublereal dmax__;
static integer i__, ix;
/* finds the index of element having max. absolute value.
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
Parameter adjustments */
--dx;
/* Function Body */
ret_val = 0;
if (*n < 1 || *incx <= 0) {
return ret_val;
}
ret_val = 1;
if (*n == 1) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
dmax__ = abs(dx[1]);
ix += *incx;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if ((d__1 = dx[ix], abs(d__1)) <= dmax__) {
goto L5;
}
ret_val = i__;
dmax__ = (d__1 = dx[ix], abs(d__1));
L5:
ix += *incx;
/* L10: */
}
return ret_val;
/* code for increment equal to 1 */
L20:
dmax__ = abs(dx[1]);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if ((d__1 = dx[i__], abs(d__1)) <= dmax__) {
goto L30;
}
ret_val = i__;
dmax__ = (d__1 = dx[i__], abs(d__1));
L30:
;
}
return ret_val;
} /* idamax_ */
#ifdef _cpluscplus
}
#endif

88
ext/f2c_blas/isamax.c Normal file
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/* isamax.f -- translated by f2c (version 20031025).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "f2c.h"
integer isamax_(integer *n, real *sx, integer *incx)
{
/* System generated locals */
integer ret_val, i__1;
real r__1;
/* Local variables */
static integer i__, ix;
static real smax;
/* finds the index of element having max. absolute value. */
/* jack dongarra, linpack, 3/11/78. */
/* modified 3/93 to return if incx .le. 0. */
/* modified 12/3/93, array(1) declarations changed to array(*) */
/* Parameter adjustments */
--sx;
/* Function Body */
ret_val = 0;
if (*n < 1 || *incx <= 0) {
return ret_val;
}
ret_val = 1;
if (*n == 1) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
smax = dabs(sx[1]);
ix += *incx;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if ((r__1 = sx[ix], dabs(r__1)) <= smax) {
goto L5;
}
ret_val = i__;
smax = (r__1 = sx[ix], dabs(r__1));
L5:
ix += *incx;
/* L10: */
}
return ret_val;
/* code for increment equal to 1 */
L20:
smax = dabs(sx[1]);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if ((r__1 = sx[i__], dabs(r__1)) <= smax) {
goto L30;
}
ret_val = i__;
smax = (r__1 = sx[i__], dabs(r__1));
L30:
;
}
return ret_val;
} /* isamax_ */
#ifdef __cplusplus
}
#endif

107
ext/f2c_blas/lsame.c Normal file
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#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
logical lsame_(char *ca, char *cb)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
LSAME returns .TRUE. if CA is the same letter as CB regardless of
case.
Arguments
=========
CA (input) CHARACTER*1
CB (input) CHARACTER*1
CA and CB specify the single characters to be compared.
=====================================================================
Test if the characters are equal */
/* System generated locals */
logical ret_val;
/* Local variables */
static integer inta, intb, zcode;
ret_val = *(unsigned char *)ca == *(unsigned char *)cb;
if (ret_val) {
return ret_val;
}
/* Now test for equivalence if both characters are alphabetic. */
zcode = 'Z';
/* Use 'Z' rather than 'A' so that ASCII can be detected on Prime
machines, on which ICHAR returns a value with bit 8 set.
ICHAR('A') on Prime machines returns 193 which is the same as
ICHAR('A') on an EBCDIC machine. */
inta = *(unsigned char *)ca;
intb = *(unsigned char *)cb;
if (zcode == 90 || zcode == 122) {
/* ASCII is assumed - ZCODE is the ASCII code of either lower o
r
upper case 'Z'. */
if (inta >= 97 && inta <= 122) {
inta += -32;
}
if (intb >= 97 && intb <= 122) {
intb += -32;
}
} else if (zcode == 233 || zcode == 169) {
/* EBCDIC is assumed - ZCODE is the EBCDIC code of either lower
or
upper case 'Z'. */
if (inta >= 129 && inta <= 137 || inta >= 145 && inta <= 153 || inta
>= 162 && inta <= 169) {
inta += 64;
}
if (intb >= 129 && intb <= 137 || intb >= 145 && intb <= 153 || intb
>= 162 && intb <= 169) {
intb += 64;
}
} else if (zcode == 218 || zcode == 250) {
/* ASCII is assumed, on Prime machines - ZCODE is the ASCII cod
e
plus 128 of either lower or upper case 'Z'. */
if (inta >= 225 && inta <= 250) {
inta += -32;
}
if (intb >= 225 && intb <= 250) {
intb += -32;
}
}
ret_val = inta == intb;
/* RETURN
End of LSAME */
return ret_val;
} /* lsame_ */
#ifdef _cpluscplus
}
#endif

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ext/f2c_blas/xerbla.c Normal file
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#include "blaswrap.h"
#ifdef _cpluscplus
extern "C" {
#endif
#include "f2c.h"
/* Subroutine */ int xerbla_(char *srname, integer *info)
{
/* -- LAPACK auxiliary routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
XERBLA is an error handler for the LAPACK routines.
It is called by an LAPACK routine if an input parameter has an
invalid value. A message is printed and execution stops.
Installers may consider modifying the STOP statement in order to
call system-specific exception-handling facilities.
Arguments
=========
SRNAME (input) CHARACTER*6
The name of the routine which called XERBLA.
INFO (input) INTEGER
The position of the invalid parameter in the parameter list
of the calling routine.
=====================================================================
*/
printf("** On entry to %6s, parameter number %2i had an illegal value\n",
srname, *info);
/* End of XERBLA */
return 0;
} /* xerbla_ */
#ifdef _cpluscplus
}
#endif