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Diffstat (limited to 'src/lib/lapack/zgebd2.f')
| -rw-r--r-- | src/lib/lapack/zgebd2.f | 250 |
1 files changed, 0 insertions, 250 deletions
diff --git a/src/lib/lapack/zgebd2.f b/src/lib/lapack/zgebd2.f deleted file mode 100644 index 5ba52e87..00000000 --- a/src/lib/lapack/zgebd2.f +++ /dev/null @@ -1,250 +0,0 @@ - SUBROUTINE ZGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO ) -* -* -- LAPACK routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), E( * ) - COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * ) -* .. -* -* Purpose -* ======= -* -* ZGEBD2 reduces a complex general m by n matrix A to upper or lower -* real bidiagonal form B by a unitary transformation: Q' * 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) COMPLEX*16 array, dimension (max(M,N)) -* -* 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, 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 ZERO, ONE - PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), - $ ONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - INTEGER I - COMPLEX*16 ALPHA -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLACGV, ZLARF, ZLARFG -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG, MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - 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 - END IF - IF( INFO.LT.0 ) THEN - CALL XERBLA( 'ZGEBD2', -INFO ) - RETURN - END IF -* - IF( M.GE.N ) THEN -* -* Reduce to upper bidiagonal form -* - DO 10 I = 1, N -* -* Generate elementary reflector H(i) to annihilate A(i+1:m,i) -* - ALPHA = A( I, I ) - CALL ZLARFG( M-I+1, ALPHA, A( MIN( I+1, M ), I ), 1, - $ TAUQ( I ) ) - D( I ) = ALPHA - A( I, I ) = ONE -* -* Apply H(i)' to A(i:m,i+1:n) from the left -* - IF( I.LT.N ) - $ CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, - $ DCONJG( TAUQ( I ) ), A( I, I+1 ), LDA, WORK ) - A( I, I ) = D( I ) -* - IF( I.LT.N ) THEN -* -* Generate elementary reflector G(i) to annihilate -* A(i,i+2:n) -* - CALL ZLACGV( N-I, A( I, I+1 ), LDA ) - ALPHA = A( I, I+1 ) - CALL ZLARFG( N-I, ALPHA, A( I, MIN( I+2, N ) ), LDA, - $ TAUP( I ) ) - E( I ) = ALPHA - A( I, I+1 ) = ONE -* -* Apply G(i) to A(i+1:m,i+1:n) from the right -* - CALL ZLARF( 'Right', M-I, N-I, A( I, I+1 ), LDA, - $ TAUP( I ), A( I+1, I+1 ), LDA, WORK ) - CALL ZLACGV( N-I, A( I, I+1 ), LDA ) - A( I, I+1 ) = E( I ) - ELSE - TAUP( I ) = ZERO - END IF - 10 CONTINUE - ELSE -* -* Reduce to lower bidiagonal form -* - DO 20 I = 1, M -* -* Generate elementary reflector G(i) to annihilate A(i,i+1:n) -* - CALL ZLACGV( N-I+1, A( I, I ), LDA ) - ALPHA = A( I, I ) - CALL ZLARFG( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA, - $ TAUP( I ) ) - D( I ) = ALPHA - A( I, I ) = ONE -* -* Apply G(i) to A(i+1:m,i:n) from the right -* - IF( I.LT.M ) - $ CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, - $ TAUP( I ), A( I+1, I ), LDA, WORK ) - CALL ZLACGV( N-I+1, A( I, I ), LDA ) - A( I, I ) = D( I ) -* - IF( I.LT.M ) THEN -* -* Generate elementary reflector H(i) to annihilate -* A(i+2:m,i) -* - ALPHA = A( I+1, I ) - CALL ZLARFG( M-I, ALPHA, A( MIN( I+2, M ), I ), 1, - $ TAUQ( I ) ) - E( I ) = ALPHA - A( I+1, I ) = ONE -* -* Apply H(i)' to A(i+1:m,i+1:n) from the left -* - CALL ZLARF( 'Left', M-I, N-I, A( I+1, I ), 1, - $ DCONJG( TAUQ( I ) ), A( I+1, I+1 ), LDA, - $ WORK ) - A( I+1, I ) = E( I ) - ELSE - TAUQ( I ) = ZERO - END IF - 20 CONTINUE - END IF - RETURN -* -* End of ZGEBD2 -* - END |