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SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
* * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER VECT INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * DORGBR generates one of the real orthogonal matrices Q or P**T * determined by DGEBRD when reducing a real matrix A to bidiagonal * form: A = Q * B * P**T. Q and P**T are defined as products of * elementary reflectors H(i) or G(i) respectively. * * If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q * is of order M: * if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n * columns of Q, where m >= n >= k; * if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an * M-by-M matrix. * * If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T * is of order N: * if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m * rows of P**T, where n >= m >= k; * if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as * an N-by-N matrix. * * Arguments * ========= * * VECT (input) CHARACTER*1 * Specifies whether the matrix Q or the matrix P**T is * required, as defined in the transformation applied by DGEBRD: * = 'Q': generate Q; * = 'P': generate P**T. * * M (input) INTEGER * The number of rows of the matrix Q or P**T to be returned. * M >= 0. * * N (input) INTEGER * The number of columns of the matrix Q or P**T to be returned. * N >= 0. * If VECT = 'Q', M >= N >= min(M,K); * if VECT = 'P', N >= M >= min(N,K). * * K (input) INTEGER * If VECT = 'Q', the number of columns in the original M-by-K * matrix reduced by DGEBRD. * If VECT = 'P', the number of rows in the original K-by-N * matrix reduced by DGEBRD. * K >= 0. * * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) * On entry, the vectors which define the elementary reflectors, * as returned by DGEBRD. * On exit, the M-by-N matrix Q or P**T. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,M). * * TAU (input) DOUBLE PRECISION array, dimension * (min(M,K)) if VECT = 'Q' * (min(N,K)) if VECT = 'P' * TAU(i) must contain the scalar factor of the elementary * reflector H(i) or G(i), which determines Q or P**T, as * returned by DGEBRD in its array argument TAUQ or TAUP. * * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. * * LWORK (input) INTEGER * The dimension of the array WORK. LWORK >= max(1,min(M,N)). * For optimum performance LWORK >= min(M,N)*NB, where NB * is the optimal blocksize. * * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the optimal size of the WORK array, returns * this value as the first entry of the WORK array, and no error * message related to LWORK is issued by XERBLA. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY, WANTQ INTEGER I, IINFO, J, LWKOPT, MN, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DORGLQ, DORGQR, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 WANTQ = LSAME( VECT, 'Q' ) MN = MIN( M, N ) LQUERY = ( LWORK.EQ.-1 ) IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN INFO = -1 ELSE IF( M.LT.0 ) THEN INFO = -2 ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M, $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT. $ MIN( N, K ) ) ) ) THEN INFO = -3 ELSE IF( K.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -6 ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN INFO = -9 END IF * IF( INFO.EQ.0 ) THEN IF( WANTQ ) THEN NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) ELSE NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 ) END IF LWKOPT = MAX( 1, MN )*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORGBR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * IF( WANTQ ) THEN * * Form Q, determined by a call to DGEBRD to reduce an m-by-k * matrix * IF( M.GE.K ) THEN * * If m >= k, assume m >= n >= k * CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) * ELSE * * If m < k, assume m = n * * Shift the vectors which define the elementary reflectors one * column to the right, and set the first row and column of Q * to those of the unit matrix * DO 20 J = M, 2, -1 A( 1, J ) = ZERO DO 10 I = J + 1, M A( I, J ) = A( I, J-1 ) 10 CONTINUE 20 CONTINUE A( 1, 1 ) = ONE DO 30 I = 2, M A( I, 1 ) = ZERO 30 CONTINUE IF( M.GT.1 ) THEN * * Form Q(2:m,2:m) * CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, $ LWORK, IINFO ) END IF END IF ELSE * * Form P**T, determined by a call to DGEBRD to reduce a k-by-n * matrix * IF( K.LT.N ) THEN * * If k < n, assume k <= m <= n * CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) * ELSE * * If k >= n, assume m = n * * Shift the vectors which define the elementary reflectors one * row downward, and set the first row and column of P**T to * those of the unit matrix * A( 1, 1 ) = ONE DO 40 I = 2, N A( I, 1 ) = ZERO 40 CONTINUE DO 60 J = 2, N DO 50 I = J - 1, 2, -1 A( I, J ) = A( I-1, J ) 50 CONTINUE A( 1, J ) = ZERO 60 CONTINUE IF( N.GT.1 ) THEN * * Form P**T(2:n,2:n) * CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, $ LWORK, IINFO ) END IF END IF END IF WORK( 1 ) = LWKOPT RETURN * * End of DORGBR * END |