223 lines
6.7 KiB
Fortran
223 lines
6.7 KiB
Fortran
SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
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*
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* -- LAPACK routine (version 2.0) --
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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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* September 30, 1994
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*
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* .. Scalar Arguments ..
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CHARACTER VECT
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INTEGER INFO, K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )
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* ..
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*
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* Purpose
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* =======
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*
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* DORGBR generates one of the real orthogonal matrices Q or P**T
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* determined by DGEBRD when reducing a real matrix A to bidiagonal
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* form: A = Q * B * P**T. Q and P**T are defined as products of
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* elementary reflectors H(i) or G(i) respectively.
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*
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* If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
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* is of order M:
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* if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
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* columns of Q, where m >= n >= k;
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* if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
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* M-by-M matrix.
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*
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* If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
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* is of order N:
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* if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
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* rows of P**T, where n >= m >= k;
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* if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
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* an N-by-N matrix.
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*
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* Arguments
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* =========
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*
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* VECT (input) CHARACTER*1
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* Specifies whether the matrix Q or the matrix P**T is
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* required, as defined in the transformation applied by DGEBRD:
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* = 'Q': generate Q;
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* = 'P': generate P**T.
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*
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* M (input) INTEGER
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* The number of rows of the matrix Q or P**T to be returned.
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* M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix Q or P**T to be returned.
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* N >= 0.
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* If VECT = 'Q', M >= N >= min(M,K);
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* if VECT = 'P', N >= M >= min(N,K).
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*
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* K (input) INTEGER
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* If VECT = 'Q', the number of columns in the original M-by-K
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* matrix reduced by DGEBRD.
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* If VECT = 'P', the number of rows in the original K-by-N
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* matrix reduced by DGEBRD.
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* K >= 0.
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*
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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* On entry, the vectors which define the elementary reflectors,
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* as returned by DGEBRD.
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* On exit, the M-by-N matrix Q or P**T.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,M).
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*
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* TAU (input) DOUBLE PRECISION array, dimension
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* (min(M,K)) if VECT = 'Q'
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* (min(N,K)) if VECT = 'P'
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* TAU(i) must contain the scalar factor of the elementary
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* reflector H(i) or G(i), which determines Q or P**T, as
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* returned by DGEBRD in its array argument TAUQ or TAUP.
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*
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* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*
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* LWORK (input) INTEGER
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* The dimension of the array WORK. LWORK >= max(1,min(M,N)).
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* For optimum performance LWORK >= min(M,N)*NB, where NB
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* is the optimal blocksize.
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL WANTQ
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INTEGER I, IINFO, J
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL DORGLQ, DORGQR, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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WANTQ = LSAME( VECT, 'Q' )
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IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
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INFO = -1
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ELSE IF( M.LT.0 ) THEN
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INFO = -2
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ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
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$ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
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$ MIN( N, K ) ) ) ) THEN
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INFO = -3
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ELSE IF( K.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -6
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ELSE IF( LWORK.LT.MAX( 1, MIN( M, N ) ) ) THEN
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INFO = -9
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DORGBR', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.EQ.0 .OR. N.EQ.0 ) THEN
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WORK( 1 ) = 1
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RETURN
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END IF
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*
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IF( WANTQ ) THEN
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*
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* Form Q, determined by a call to DGEBRD to reduce an m-by-k
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* matrix
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*
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IF( M.GE.K ) THEN
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*
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* If m >= k, assume m >= n >= k
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*
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CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
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*
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ELSE
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*
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* If m < k, assume m = n
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*
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* Shift the vectors which define the elementary reflectors one
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* column to the right, and set the first row and column of Q
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* to those of the unit matrix
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*
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DO 20 J = M, 2, -1
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A( 1, J ) = ZERO
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DO 10 I = J + 1, M
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A( I, J ) = A( I, J-1 )
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10 CONTINUE
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20 CONTINUE
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A( 1, 1 ) = ONE
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DO 30 I = 2, M
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A( I, 1 ) = ZERO
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30 CONTINUE
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IF( M.GT.1 ) THEN
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*
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* Form Q(2:m,2:m)
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*
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CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
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$ LWORK, IINFO )
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END IF
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END IF
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ELSE
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*
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* Form P', determined by a call to DGEBRD to reduce a k-by-n
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* matrix
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*
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IF( K.LT.N ) THEN
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*
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* If k < n, assume k <= m <= n
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*
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CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
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*
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ELSE
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*
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* If k >= n, assume m = n
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*
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* Shift the vectors which define the elementary reflectors one
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* row downward, and set the first row and column of P' to
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* those of the unit matrix
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*
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A( 1, 1 ) = ONE
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DO 40 I = 2, N
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A( I, 1 ) = ZERO
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40 CONTINUE
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DO 60 J = 2, N
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DO 50 I = J - 1, 2, -1
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A( I, J ) = A( I-1, J )
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50 CONTINUE
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A( 1, J ) = ZERO
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60 CONTINUE
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IF( N.GT.1 ) THEN
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*
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* Form P'(2:n,2:n)
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*
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CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
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$ LWORK, IINFO )
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END IF
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END IF
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END IF
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RETURN
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*
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* End of DORGBR
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*
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END
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