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Diffstat (limited to 'src/lib/lapack/dlabrd.f')
| -rw-r--r-- | src/lib/lapack/dlabrd.f | 290 |
1 files changed, 0 insertions, 290 deletions
diff --git a/src/lib/lapack/dlabrd.f b/src/lib/lapack/dlabrd.f deleted file mode 100644 index 196b130c..00000000 --- a/src/lib/lapack/dlabrd.f +++ /dev/null @@ -1,290 +0,0 @@ - SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, - $ LDY ) -* -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDX, LDY, M, N, NB -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), - $ TAUQ( * ), X( LDX, * ), Y( LDY, * ) -* .. -* -* Purpose -* ======= -* -* DLABRD reduces the first NB rows and columns of a real general -* m by n matrix A to upper or lower bidiagonal form by an orthogonal -* transformation Q' * A * P, and returns the matrices X and Y which -* are needed to apply the transformation to the unreduced part of A. -* -* If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower -* bidiagonal form. -* -* This is an auxiliary routine called by DGEBRD -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows in the matrix A. -* -* N (input) INTEGER -* The number of columns in the matrix A. -* -* NB (input) INTEGER -* The number of leading rows and columns of A to be reduced. -* -* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -* On entry, the m by n general matrix to be reduced. -* On exit, the first NB rows and columns of the matrix are -* overwritten; the rest of the array is unchanged. -* If m >= n, elements on and below the diagonal in the first NB -* columns, with the array TAUQ, represent the orthogonal -* matrix Q as a product of elementary reflectors; and -* elements above the diagonal in the first NB rows, with the -* array TAUP, represent the orthogonal matrix P as a product -* of elementary reflectors. -* If m < n, elements below the diagonal in the first NB -* columns, with the array TAUQ, represent the orthogonal -* matrix Q as a product of elementary reflectors, and -* elements on and above the diagonal in the first NB rows, -* with the array TAUP, represent the orthogonal 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 (NB) -* The diagonal elements of the first NB rows and columns of -* the reduced matrix. D(i) = A(i,i). -* -* E (output) DOUBLE PRECISION array, dimension (NB) -* The off-diagonal elements of the first NB rows and columns of -* the reduced matrix. -* -* TAUQ (output) DOUBLE PRECISION array dimension (NB) -* The scalar factors of the elementary reflectors which -* represent the orthogonal matrix Q. See Further Details. -* -* TAUP (output) DOUBLE PRECISION array, dimension (NB) -* The scalar factors of the elementary reflectors which -* represent the orthogonal matrix P. See Further Details. -* -* X (output) DOUBLE PRECISION array, dimension (LDX,NB) -* The m-by-nb matrix X required to update the unreduced part -* of A. -* -* LDX (input) INTEGER -* The leading dimension of the array X. LDX >= M. -* -* Y (output) DOUBLE PRECISION array, dimension (LDY,NB) -* The n-by-nb matrix Y required to update the unreduced part -* of A. -* -* LDY (input) INTEGER -* The leading dimension of the array Y. LDY >= N. -* -* Further Details -* =============== -* -* The matrices Q and P are represented as products of elementary -* reflectors: -* -* Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) -* -* 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 real scalars, and v and u are real vectors. -* -* If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in -* A(i:m,i); u(1:i) = 0, u(i+1) = 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). -* -* If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in -* A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in -* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). -* -* The elements of the vectors v and u together form the m-by-nb matrix -* V and the nb-by-n matrix U' which are needed, with X and Y, to apply -* the transformation to the unreduced part of the matrix, using a block -* update of the form: A := A - V*Y' - X*U'. -* -* The contents of A on exit are illustrated by the following examples -* with nb = 2: -* -* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): -* -* ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) -* ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) -* ( v1 v2 a a a ) ( v1 1 a a a a ) -* ( v1 v2 a a a ) ( v1 v2 a a a a ) -* ( v1 v2 a a a ) ( v1 v2 a a a a ) -* ( v1 v2 a a a ) -* -* where a denotes an element of the original matrix which is unchanged, -* vi denotes an element of the vector defining H(i), and ui an element -* of the vector defining G(i). -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - INTEGER I -* .. -* .. External Subroutines .. - EXTERNAL DGEMV, DLARFG, DSCAL -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( M.LE.0 .OR. N.LE.0 ) - $ RETURN -* - IF( M.GE.N ) THEN -* -* Reduce to upper bidiagonal form -* - DO 10 I = 1, NB -* -* Update A(i:m,i) -* - CALL DGEMV( 'No transpose', M-I+1, I-1, -ONE, A( I, 1 ), - $ LDA, Y( I, 1 ), LDY, ONE, A( I, I ), 1 ) - CALL DGEMV( 'No transpose', M-I+1, I-1, -ONE, X( I, 1 ), - $ LDX, A( 1, I ), 1, ONE, A( I, I ), 1 ) -* -* Generate reflection Q(i) to annihilate A(i+1:m,i) -* - CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, - $ TAUQ( I ) ) - D( I ) = A( I, I ) - IF( I.LT.N ) THEN - A( I, I ) = ONE -* -* Compute Y(i+1:n,i) -* - CALL DGEMV( 'Transpose', M-I+1, N-I, ONE, A( I, I+1 ), - $ LDA, A( I, I ), 1, ZERO, Y( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', M-I+1, I-1, ONE, A( I, 1 ), LDA, - $ A( I, I ), 1, ZERO, Y( 1, I ), 1 ) - CALL DGEMV( 'No transpose', N-I, I-1, -ONE, Y( I+1, 1 ), - $ LDY, Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', M-I+1, I-1, ONE, X( I, 1 ), LDX, - $ A( I, I ), 1, ZERO, Y( 1, I ), 1 ) - CALL DGEMV( 'Transpose', I-1, N-I, -ONE, A( 1, I+1 ), - $ LDA, Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) - CALL DSCAL( N-I, TAUQ( I ), Y( I+1, I ), 1 ) -* -* Update A(i,i+1:n) -* - CALL DGEMV( 'No transpose', N-I, I, -ONE, Y( I+1, 1 ), - $ LDY, A( I, 1 ), LDA, ONE, A( I, I+1 ), LDA ) - CALL DGEMV( 'Transpose', I-1, N-I, -ONE, A( 1, I+1 ), - $ LDA, X( I, 1 ), LDX, ONE, A( I, I+1 ), LDA ) -* -* Generate reflection P(i) to annihilate A(i,i+2:n) -* - CALL DLARFG( N-I, A( I, I+1 ), A( I, MIN( I+2, N ) ), - $ LDA, TAUP( I ) ) - E( I ) = A( I, I+1 ) - A( I, I+1 ) = ONE -* -* Compute X(i+1:m,i) -* - CALL DGEMV( 'No transpose', M-I, N-I, ONE, A( I+1, I+1 ), - $ LDA, A( I, I+1 ), LDA, ZERO, X( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', N-I, I, ONE, Y( I+1, 1 ), LDY, - $ A( I, I+1 ), LDA, ZERO, X( 1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I, -ONE, A( I+1, 1 ), - $ LDA, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) - CALL DGEMV( 'No transpose', I-1, N-I, ONE, A( 1, I+1 ), - $ LDA, A( I, I+1 ), LDA, ZERO, X( 1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I-1, -ONE, X( I+1, 1 ), - $ LDX, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) - CALL DSCAL( M-I, TAUP( I ), X( I+1, I ), 1 ) - END IF - 10 CONTINUE - ELSE -* -* Reduce to lower bidiagonal form -* - DO 20 I = 1, NB -* -* Update A(i,i:n) -* - CALL DGEMV( 'No transpose', N-I+1, I-1, -ONE, Y( I, 1 ), - $ LDY, A( I, 1 ), LDA, ONE, A( I, I ), LDA ) - CALL DGEMV( 'Transpose', I-1, N-I+1, -ONE, A( 1, I ), LDA, - $ X( I, 1 ), LDX, ONE, A( I, I ), LDA ) -* -* Generate reflection P(i) to annihilate A(i,i+1:n) -* - CALL DLARFG( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA, - $ TAUP( I ) ) - D( I ) = A( I, I ) - IF( I.LT.M ) THEN - A( I, I ) = ONE -* -* Compute X(i+1:m,i) -* - CALL DGEMV( 'No transpose', M-I, N-I+1, ONE, A( I+1, I ), - $ LDA, A( I, I ), LDA, ZERO, X( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', N-I+1, I-1, ONE, Y( I, 1 ), LDY, - $ A( I, I ), LDA, ZERO, X( 1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I-1, -ONE, A( I+1, 1 ), - $ LDA, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) - CALL DGEMV( 'No transpose', I-1, N-I+1, ONE, A( 1, I ), - $ LDA, A( I, I ), LDA, ZERO, X( 1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I-1, -ONE, X( I+1, 1 ), - $ LDX, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) - CALL DSCAL( M-I, TAUP( I ), X( I+1, I ), 1 ) -* -* Update A(i+1:m,i) -* - CALL DGEMV( 'No transpose', M-I, I-1, -ONE, A( I+1, 1 ), - $ LDA, Y( I, 1 ), LDY, ONE, A( I+1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I, -ONE, X( I+1, 1 ), - $ LDX, A( 1, I ), 1, ONE, A( I+1, I ), 1 ) -* -* Generate reflection Q(i) to annihilate A(i+2:m,i) -* - CALL DLARFG( M-I, A( I+1, I ), A( MIN( I+2, M ), I ), 1, - $ TAUQ( I ) ) - E( I ) = A( I+1, I ) - A( I+1, I ) = ONE -* -* Compute Y(i+1:n,i) -* - CALL DGEMV( 'Transpose', M-I, N-I, ONE, A( I+1, I+1 ), - $ LDA, A( I+1, I ), 1, ZERO, Y( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', M-I, I-1, ONE, A( I+1, 1 ), LDA, - $ A( I+1, I ), 1, ZERO, Y( 1, I ), 1 ) - CALL DGEMV( 'No transpose', N-I, I-1, -ONE, Y( I+1, 1 ), - $ LDY, Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', M-I, I, ONE, X( I+1, 1 ), LDX, - $ A( I+1, I ), 1, ZERO, Y( 1, I ), 1 ) - CALL DGEMV( 'Transpose', I, N-I, -ONE, A( 1, I+1 ), LDA, - $ Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) - CALL DSCAL( N-I, TAUQ( I ), Y( I+1, I ), 1 ) - END IF - 20 CONTINUE - END IF - RETURN -* -* End of DLABRD -* - END |