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Diffstat (limited to '2.3-1/src/fortran/lapack/zgebrd.f')
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diff --git a/2.3-1/src/fortran/lapack/zgebrd.f b/2.3-1/src/fortran/lapack/zgebrd.f new file mode 100644 index 00000000..4f97bd7e --- /dev/null +++ b/2.3-1/src/fortran/lapack/zgebrd.f @@ -0,0 +1,268 @@ + SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, + $ INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, LWORK, M, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION D( * ), E( * ) + COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* ZGEBRD reduces a general complex M-by-N matrix A to upper or lower +* bidiagonal form B by a unitary transformation: Q**H * A * P = B. +* +* If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows in the matrix A. M >= 0. +* +* N (input) INTEGER +* The number of columns in the matrix A. N >= 0. +* +* A (input/output) COMPLEX*16 array, dimension (LDA,N) +* On entry, the M-by-N general matrix to be reduced. +* On exit, +* if m >= n, the diagonal and the first superdiagonal are +* overwritten with the upper bidiagonal matrix B; the +* elements below the diagonal, with the array TAUQ, represent +* the unitary matrix Q as a product of elementary +* reflectors, and the elements above the first superdiagonal, +* with the array TAUP, represent the unitary matrix P as +* a product of elementary reflectors; +* if m < n, the diagonal and the first subdiagonal are +* overwritten with the lower bidiagonal matrix B; the +* elements below the first subdiagonal, with the array TAUQ, +* represent the unitary matrix Q as a product of +* elementary reflectors, and the elements above the diagonal, +* with the array TAUP, represent the unitary matrix P as +* a product of elementary reflectors. +* See Further Details. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* D (output) DOUBLE PRECISION array, dimension (min(M,N)) +* The diagonal elements of the bidiagonal matrix B: +* D(i) = A(i,i). +* +* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) +* The off-diagonal elements of the bidiagonal matrix B: +* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; +* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. +* +* TAUQ (output) COMPLEX*16 array dimension (min(M,N)) +* The scalar factors of the elementary reflectors which +* represent the unitary matrix Q. See Further Details. +* +* TAUP (output) COMPLEX*16 array, dimension (min(M,N)) +* The scalar factors of the elementary reflectors which +* represent the unitary matrix P. See Further Details. +* +* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The length of the array WORK. LWORK >= max(1,M,N). +* For optimum performance LWORK >= (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. +* +* Further Details +* =============== +* +* The matrices Q and P are represented as products of elementary +* reflectors: +* +* If m >= n, +* +* Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) +* +* Each H(i) and G(i) has the form: +* +* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' +* +* where tauq and taup are complex scalars, and v and u are complex +* vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in +* A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in +* A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i). +* +* If m < n, +* +* Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) +* +* Each H(i) and G(i) has the form: +* +* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' +* +* where tauq and taup are complex scalars, and v and u are complex +* vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in +* A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in +* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). +* +* The contents of A on exit are illustrated by the following examples: +* +* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): +* +* ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) +* ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) +* ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) +* ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) +* ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) +* ( v1 v2 v3 v4 v5 ) +* +* where d and e denote diagonal and off-diagonal elements of B, vi +* denotes an element of the vector defining H(i), and ui an element of +* the vector defining G(i). +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY + INTEGER I, IINFO, J, LDWRKX, LDWRKY, LWKOPT, MINMN, NB, + $ NBMIN, NX + DOUBLE PRECISION WS +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZGEBD2, ZGEMM, ZLABRD +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE, MAX, MIN +* .. +* .. External Functions .. + INTEGER ILAENV + EXTERNAL ILAENV +* .. +* .. Executable Statements .. +* +* Test the input parameters +* + INFO = 0 + NB = MAX( 1, ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 ) ) + LWKOPT = ( M+N )*NB + WORK( 1 ) = DBLE( LWKOPT ) + LQUERY = ( LWORK.EQ.-1 ) + IF( M.LT.0 ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = -4 + ELSE IF( LWORK.LT.MAX( 1, M, N ) .AND. .NOT.LQUERY ) THEN + INFO = -10 + END IF + IF( INFO.LT.0 ) THEN + CALL XERBLA( 'ZGEBRD', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + MINMN = MIN( M, N ) + IF( MINMN.EQ.0 ) THEN + WORK( 1 ) = 1 + RETURN + END IF +* + WS = MAX( M, N ) + LDWRKX = M + LDWRKY = N +* + IF( NB.GT.1 .AND. NB.LT.MINMN ) THEN +* +* Set the crossover point NX. +* + NX = MAX( NB, ILAENV( 3, 'ZGEBRD', ' ', M, N, -1, -1 ) ) +* +* Determine when to switch from blocked to unblocked code. +* + IF( NX.LT.MINMN ) THEN + WS = ( M+N )*NB + IF( LWORK.LT.WS ) THEN +* +* Not enough work space for the optimal NB, consider using +* a smaller block size. +* + NBMIN = ILAENV( 2, 'ZGEBRD', ' ', M, N, -1, -1 ) + IF( LWORK.GE.( M+N )*NBMIN ) THEN + NB = LWORK / ( M+N ) + ELSE + NB = 1 + NX = MINMN + END IF + END IF + END IF + ELSE + NX = MINMN + END IF +* + DO 30 I = 1, MINMN - NX, NB +* +* Reduce rows and columns i:i+ib-1 to bidiagonal form and return +* the matrices X and Y which are needed to update the unreduced +* part of the matrix +* + CALL ZLABRD( M-I+1, N-I+1, NB, A( I, I ), LDA, D( I ), E( I ), + $ TAUQ( I ), TAUP( I ), WORK, LDWRKX, + $ WORK( LDWRKX*NB+1 ), LDWRKY ) +* +* Update the trailing submatrix A(i+ib:m,i+ib:n), using +* an update of the form A := A - V*Y' - X*U' +* + CALL ZGEMM( 'No transpose', 'Conjugate transpose', M-I-NB+1, + $ N-I-NB+1, NB, -ONE, A( I+NB, I ), LDA, + $ WORK( LDWRKX*NB+NB+1 ), LDWRKY, ONE, + $ A( I+NB, I+NB ), LDA ) + CALL ZGEMM( 'No transpose', 'No transpose', M-I-NB+1, N-I-NB+1, + $ NB, -ONE, WORK( NB+1 ), LDWRKX, A( I, I+NB ), LDA, + $ ONE, A( I+NB, I+NB ), LDA ) +* +* Copy diagonal and off-diagonal elements of B back into A +* + IF( M.GE.N ) THEN + DO 10 J = I, I + NB - 1 + A( J, J ) = D( J ) + A( J, J+1 ) = E( J ) + 10 CONTINUE + ELSE + DO 20 J = I, I + NB - 1 + A( J, J ) = D( J ) + A( J+1, J ) = E( J ) + 20 CONTINUE + END IF + 30 CONTINUE +* +* Use unblocked code to reduce the remainder of the matrix +* + CALL ZGEBD2( M-I+1, N-I+1, A( I, I ), LDA, D( I ), E( I ), + $ TAUQ( I ), TAUP( I ), WORK, IINFO ) + WORK( 1 ) = WS + RETURN +* +* End of ZGEBRD +* + END |