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Diffstat (limited to 'src/lib/lapack/dlahrd.f')
| -rw-r--r-- | src/lib/lapack/dlahrd.f | 207 |
1 files changed, 0 insertions, 207 deletions
diff --git a/src/lib/lapack/dlahrd.f b/src/lib/lapack/dlahrd.f deleted file mode 100644 index a04133d1..00000000 --- a/src/lib/lapack/dlahrd.f +++ /dev/null @@ -1,207 +0,0 @@ - SUBROUTINE DLAHRD( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) -* -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER K, LDA, LDT, LDY, N, NB -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), T( LDT, NB ), TAU( NB ), - $ Y( LDY, NB ) -* .. -* -* Purpose -* ======= -* -* DLAHRD reduces the first NB columns of a real general n-by-(n-k+1) -* matrix A so that elements below the k-th subdiagonal are zero. The -* reduction is performed by an orthogonal similarity transformation -* Q' * A * Q. The routine returns the matrices V and T which determine -* Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T. -* -* This is an OBSOLETE auxiliary routine. -* This routine will be 'deprecated' in a future release. -* Please use the new routine DLAHR2 instead. -* -* Arguments -* ========= -* -* N (input) INTEGER -* The order of the matrix A. -* -* K (input) INTEGER -* The offset for the reduction. Elements below the k-th -* subdiagonal in the first NB columns are reduced to zero. -* -* NB (input) INTEGER -* The number of columns to be reduced. -* -* A (input/output) DOUBLE PRECISION array, dimension (LDA,N-K+1) -* On entry, the n-by-(n-k+1) general matrix A. -* On exit, the elements on and above the k-th subdiagonal in -* the first NB columns are overwritten with the corresponding -* elements of the reduced matrix; the elements below the k-th -* subdiagonal, with the array TAU, represent the matrix Q as a -* product of elementary reflectors. The other columns of A are -* unchanged. See Further Details. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,N). -* -* TAU (output) DOUBLE PRECISION array, dimension (NB) -* The scalar factors of the elementary reflectors. See Further -* Details. -* -* T (output) DOUBLE PRECISION array, dimension (LDT,NB) -* The upper triangular matrix T. -* -* LDT (input) INTEGER -* The leading dimension of the array T. LDT >= NB. -* -* Y (output) DOUBLE PRECISION array, dimension (LDY,NB) -* The n-by-nb matrix Y. -* -* LDY (input) INTEGER -* The leading dimension of the array Y. LDY >= N. -* -* Further Details -* =============== -* -* The matrix Q is represented as a product of nb elementary reflectors -* -* Q = H(1) H(2) . . . H(nb). -* -* Each H(i) has the form -* -* H(i) = I - tau * v * v' -* -* where tau is a real scalar, and v is a real vector with -* v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in -* A(i+k+1:n,i), and tau in TAU(i). -* -* The elements of the vectors v together form the (n-k+1)-by-nb matrix -* V which is needed, with T and Y, to apply the transformation to the -* unreduced part of the matrix, using an update of the form: -* A := (I - V*T*V') * (A - Y*V'). -* -* The contents of A on exit are illustrated by the following example -* with n = 7, k = 3 and nb = 2: -* -* ( a h a a a ) -* ( a h a a a ) -* ( a h a a a ) -* ( h h a a a ) -* ( v1 h a a a ) -* ( v1 v2 a a a ) -* ( v1 v2 a a a ) -* -* where a denotes an element of the original matrix A, h denotes a -* modified element of the upper Hessenberg matrix H, and vi denotes an -* element of the vector defining H(i). -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I - DOUBLE PRECISION EI -* .. -* .. External Subroutines .. - EXTERNAL DAXPY, DCOPY, DGEMV, DLARFG, DSCAL, DTRMV -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( N.LE.1 ) - $ RETURN -* - DO 10 I = 1, NB - IF( I.GT.1 ) THEN -* -* Update A(1:n,i) -* -* Compute i-th column of A - Y * V' -* - CALL DGEMV( 'No transpose', N, I-1, -ONE, Y, LDY, - $ A( K+I-1, 1 ), LDA, ONE, A( 1, I ), 1 ) -* -* Apply I - V * T' * V' to this column (call it b) from the -* left, using the last column of T as workspace -* -* Let V = ( V1 ) and b = ( b1 ) (first I-1 rows) -* ( V2 ) ( b2 ) -* -* where V1 is unit lower triangular -* -* w := V1' * b1 -* - CALL DCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 ) - CALL DTRMV( 'Lower', 'Transpose', 'Unit', I-1, A( K+1, 1 ), - $ LDA, T( 1, NB ), 1 ) -* -* w := w + V2'*b2 -* - CALL DGEMV( 'Transpose', N-K-I+1, I-1, ONE, A( K+I, 1 ), - $ LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 ) -* -* w := T'*w -* - CALL DTRMV( 'Upper', 'Transpose', 'Non-unit', I-1, T, LDT, - $ T( 1, NB ), 1 ) -* -* b2 := b2 - V2*w -* - CALL DGEMV( 'No transpose', N-K-I+1, I-1, -ONE, A( K+I, 1 ), - $ LDA, T( 1, NB ), 1, ONE, A( K+I, I ), 1 ) -* -* b1 := b1 - V1*w -* - CALL DTRMV( 'Lower', 'No transpose', 'Unit', I-1, - $ A( K+1, 1 ), LDA, T( 1, NB ), 1 ) - CALL DAXPY( I-1, -ONE, T( 1, NB ), 1, A( K+1, I ), 1 ) -* - A( K+I-1, I-1 ) = EI - END IF -* -* Generate the elementary reflector H(i) to annihilate -* A(k+i+1:n,i) -* - CALL DLARFG( N-K-I+1, A( K+I, I ), A( MIN( K+I+1, N ), I ), 1, - $ TAU( I ) ) - EI = A( K+I, I ) - A( K+I, I ) = ONE -* -* Compute Y(1:n,i) -* - CALL DGEMV( 'No transpose', N, N-K-I+1, ONE, A( 1, I+1 ), LDA, - $ A( K+I, I ), 1, ZERO, Y( 1, I ), 1 ) - CALL DGEMV( 'Transpose', N-K-I+1, I-1, ONE, A( K+I, 1 ), LDA, - $ A( K+I, I ), 1, ZERO, T( 1, I ), 1 ) - CALL DGEMV( 'No transpose', N, I-1, -ONE, Y, LDY, T( 1, I ), 1, - $ ONE, Y( 1, I ), 1 ) - CALL DSCAL( N, TAU( I ), Y( 1, I ), 1 ) -* -* Compute T(1:i,i) -* - CALL DSCAL( I-1, -TAU( I ), T( 1, I ), 1 ) - CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, LDT, - $ T( 1, I ), 1 ) - T( I, I ) = TAU( I ) -* - 10 CONTINUE - A( K+NB, NB ) = EI -* - RETURN -* -* End of DLAHRD -* - END |