401 lines
10 KiB
C
401 lines
10 KiB
C
/* dlantr.f -- translated by f2c (version 20031025).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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doublereal dlantr_(char *norm, char *uplo, char *diag, integer *m, integer *n,
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doublereal *a, integer *lda, doublereal *work, ftnlen norm_len,
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ftnlen uplo_len, ftnlen diag_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
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doublereal ret_val, d__1, d__2, d__3;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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static integer i__, j;
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static doublereal sum, scale;
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static logical udiag;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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static doublereal value;
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extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *,
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doublereal *, doublereal *);
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/* -- LAPACK auxiliary routine (version 3.0) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
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/* Courant Institute, Argonne National Lab, and Rice University */
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/* October 31, 1992 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DLANTR returns the value of the one norm, or the Frobenius norm, or */
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/* the infinity norm, or the element of largest absolute value of a */
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/* trapezoidal or triangular matrix A. */
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/* Description */
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/* =========== */
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/* DLANTR returns the value */
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/* DLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm' */
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/* ( */
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/* ( norm1(A), NORM = '1', 'O' or 'o' */
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/* ( */
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/* ( normI(A), NORM = 'I' or 'i' */
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/* ( */
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/* ( normF(A), NORM = 'F', 'f', 'E' or 'e' */
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/* where norm1 denotes the one norm of a matrix (maximum column sum), */
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/* normI denotes the infinity norm of a matrix (maximum row sum) and */
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/* normF denotes the Frobenius norm of a matrix (square root of sum of */
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/* squares). Note that max(abs(A(i,j))) is not a matrix norm. */
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/* Arguments */
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/* ========= */
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/* NORM (input) CHARACTER*1 */
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/* Specifies the value to be returned in DLANTR as described */
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/* above. */
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/* UPLO (input) CHARACTER*1 */
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/* Specifies whether the matrix A is upper or lower trapezoidal. */
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/* = 'U': Upper trapezoidal */
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/* = 'L': Lower trapezoidal */
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/* Note that A is triangular instead of trapezoidal if M = N. */
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/* DIAG (input) CHARACTER*1 */
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/* Specifies whether or not the matrix A has unit diagonal. */
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/* = 'N': Non-unit diagonal */
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/* = 'U': Unit diagonal */
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/* M (input) INTEGER */
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/* The number of rows of the matrix A. M >= 0, and if */
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/* UPLO = 'U', M <= N. When M = 0, DLANTR is set to zero. */
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/* N (input) INTEGER */
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/* The number of columns of the matrix A. N >= 0, and if */
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/* UPLO = 'L', N <= M. When N = 0, DLANTR is set to zero. */
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/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
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/* The trapezoidal matrix A (A is triangular if M = N). */
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/* If UPLO = 'U', the leading m by n upper trapezoidal part of */
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/* the array A contains the upper trapezoidal matrix, and the */
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/* strictly lower triangular part of A is not referenced. */
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/* If UPLO = 'L', the leading m by n lower trapezoidal part of */
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/* the array A contains the lower trapezoidal matrix, and the */
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/* strictly upper triangular part of A is not referenced. Note */
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/* that when DIAG = 'U', the diagonal elements of A are not */
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/* referenced and are assumed to be one. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(M,1). */
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/* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK), */
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/* where LWORK >= M when NORM = 'I'; otherwise, WORK is not */
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/* referenced. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--work;
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/* Function Body */
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if (min(*m,*n) == 0) {
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value = 0.;
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} else if (lsame_(norm, "M", (ftnlen)1, (ftnlen)1)) {
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/* Find max(abs(A(i,j))). */
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if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
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value = 1.;
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if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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/* Computing MIN */
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i__3 = *m, i__4 = j - 1;
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i__2 = min(i__3,i__4);
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for (i__ = 1; i__ <= i__2; ++i__) {
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/* Computing MAX */
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d__2 = value, d__3 = (d__1 = a[i__ + j * a_dim1], abs(
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d__1));
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value = max(d__2,d__3);
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/* L10: */
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}
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/* L20: */
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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/* Computing MAX */
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d__2 = value, d__3 = (d__1 = a[i__ + j * a_dim1], abs(
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d__1));
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value = max(d__2,d__3);
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/* L30: */
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}
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/* L40: */
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}
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}
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} else {
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value = 0.;
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if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = min(*m,j);
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for (i__ = 1; i__ <= i__2; ++i__) {
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/* Computing MAX */
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d__2 = value, d__3 = (d__1 = a[i__ + j * a_dim1], abs(
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d__1));
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value = max(d__2,d__3);
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/* L50: */
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}
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/* L60: */
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = j; i__ <= i__2; ++i__) {
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/* Computing MAX */
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d__2 = value, d__3 = (d__1 = a[i__ + j * a_dim1], abs(
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d__1));
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value = max(d__2,d__3);
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/* L70: */
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}
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/* L80: */
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}
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}
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}
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} else if (lsame_(norm, "O", (ftnlen)1, (ftnlen)1) || *(unsigned char *)
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norm == '1') {
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/* Find norm1(A). */
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value = 0.;
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udiag = lsame_(diag, "U", (ftnlen)1, (ftnlen)1);
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if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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if (udiag && j <= *m) {
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sum = 1.;
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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sum += (d__1 = a[i__ + j * a_dim1], abs(d__1));
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/* L90: */
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}
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} else {
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sum = 0.;
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i__2 = min(*m,j);
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for (i__ = 1; i__ <= i__2; ++i__) {
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sum += (d__1 = a[i__ + j * a_dim1], abs(d__1));
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/* L100: */
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}
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}
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value = max(value,sum);
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/* L110: */
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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if (udiag) {
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sum = 1.;
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i__2 = *m;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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sum += (d__1 = a[i__ + j * a_dim1], abs(d__1));
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/* L120: */
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}
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} else {
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sum = 0.;
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i__2 = *m;
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for (i__ = j; i__ <= i__2; ++i__) {
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sum += (d__1 = a[i__ + j * a_dim1], abs(d__1));
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/* L130: */
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}
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}
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value = max(value,sum);
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/* L140: */
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}
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}
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} else if (lsame_(norm, "I", (ftnlen)1, (ftnlen)1)) {
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/* Find normI(A). */
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if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
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if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
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i__1 = *m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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work[i__] = 1.;
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/* L150: */
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}
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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/* Computing MIN */
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i__3 = *m, i__4 = j - 1;
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i__2 = min(i__3,i__4);
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for (i__ = 1; i__ <= i__2; ++i__) {
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work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1));
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/* L160: */
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}
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/* L170: */
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}
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} else {
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i__1 = *m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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work[i__] = 0.;
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/* L180: */
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}
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = min(*m,j);
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for (i__ = 1; i__ <= i__2; ++i__) {
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work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1));
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/* L190: */
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}
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/* L200: */
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}
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}
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} else {
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if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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work[i__] = 1.;
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/* L210: */
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}
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i__1 = *m;
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for (i__ = *n + 1; i__ <= i__1; ++i__) {
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work[i__] = 0.;
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/* L220: */
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}
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1));
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/* L230: */
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}
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/* L240: */
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}
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} else {
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i__1 = *m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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work[i__] = 0.;
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/* L250: */
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}
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = j; i__ <= i__2; ++i__) {
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work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1));
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/* L260: */
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}
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/* L270: */
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}
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}
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}
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value = 0.;
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i__1 = *m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Computing MAX */
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d__1 = value, d__2 = work[i__];
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value = max(d__1,d__2);
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/* L280: */
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}
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} else if (lsame_(norm, "F", (ftnlen)1, (ftnlen)1) || lsame_(norm, "E", (
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ftnlen)1, (ftnlen)1)) {
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/* Find normF(A). */
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if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
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if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
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scale = 1.;
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sum = (doublereal) min(*m,*n);
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i__1 = *n;
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for (j = 2; j <= i__1; ++j) {
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/* Computing MIN */
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i__3 = *m, i__4 = j - 1;
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i__2 = min(i__3,i__4);
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dlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
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/* L290: */
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}
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} else {
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scale = 0.;
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sum = 1.;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = min(*m,j);
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dlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
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/* L300: */
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}
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}
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} else {
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if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
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scale = 1.;
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sum = (doublereal) min(*m,*n);
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m - j;
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/* Computing MIN */
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i__3 = *m, i__4 = j + 1;
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dlassq_(&i__2, &a[min(i__3,i__4) + j * a_dim1], &c__1, &
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scale, &sum);
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/* L310: */
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}
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} else {
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scale = 0.;
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sum = 1.;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m - j + 1;
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dlassq_(&i__2, &a[j + j * a_dim1], &c__1, &scale, &sum);
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/* L320: */
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}
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}
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}
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value = scale * sqrt(sum);
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}
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ret_val = value;
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return ret_val;
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/* End of DLANTR */
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} /* dlantr_ */
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