Fix typos in comments and documentation (Reference-LAPACK PR 820)
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@ -252,7 +252,7 @@
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*> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
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*> the right singular vectors;
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*> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
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*> then V is used as workspace if the pprocedure
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*> then V is used as workspace if the procedure
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*> replaces A with A^*. In that case, [U] is computed
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*> in V as right singular vectors of A^* and then
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*> copied back to the U array. This 'W' option is just
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@ -363,7 +363,7 @@
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*> an optimal implementation would do all necessary scaling before calling
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*> CGESVD and the scaling in CGESVD can be switched off.
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*> 3. Other comments related to code optimization are given in comments in the
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*> code, enlosed in [[double brackets]].
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*> code, enclosed in [[double brackets]].
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*> \endverbatim
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*
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*> \par Bugs, examples and comments
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@ -52,10 +52,10 @@
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*> Specifies whether the output from this procedure is used
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*> to compute the matrix V:
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*> = 'V': the product of the Jacobi rotations is accumulated
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*> by postmulyiplying the N-by-N array V.
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*> by postmultiplying the N-by-N array V.
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*> (See the description of V.)
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*> = 'A': the product of the Jacobi rotations is accumulated
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*> by postmulyiplying the MV-by-N array V.
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*> by postmultiplying the MV-by-N array V.
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*> (See the descriptions of MV and V.)
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*> = 'N': the Jacobi rotations are not accumulated.
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*> \endverbatim
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@ -75,10 +75,10 @@
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*> Specifies whether the output from this procedure is used
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*> to compute the matrix V:
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*> = 'V': the product of the Jacobi rotations is accumulated
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*> by postmulyiplying the N-by-N array V.
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*> by postmultiplying the N-by-N array V.
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*> (See the description of V.)
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*> = 'A': the product of the Jacobi rotations is accumulated
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*> by postmulyiplying the MV-by-N array V.
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*> by postmultiplying the MV-by-N array V.
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*> (See the descriptions of MV and V.)
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*> = 'N': the Jacobi rotations are not accumulated.
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*> \endverbatim
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@ -87,7 +87,7 @@
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*> triangular part of the matrix A, and the strictly upper
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*> triangular part of A is not referenced.
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*>
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*> On exit, L is stored below (or above) the subdiaonal blocks,
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*> On exit, L is stored below (or above) the subdiagonal blocks,
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*> when UPLO is 'L' (or 'U').
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*> \endverbatim
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*>
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@ -480,7 +480,7 @@
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A( J, K ) = CONJG( A( P, J ) )
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A( P, J ) = T
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14 CONTINUE
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* (3) Swap and conjugate corner elements at row-col interserction
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* (3) Swap and conjugate corner elements at row-col intersection
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A( P, K ) = CONJG( A( P, K ) )
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* (4) Swap diagonal elements at row-col intersection
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R1 = REAL( A( K, K ) )
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@ -508,7 +508,7 @@
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A( J, KK ) = CONJG( A( KP, J ) )
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A( KP, J ) = T
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15 CONTINUE
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* (3) Swap and conjugate corner elements at row-col interserction
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* (3) Swap and conjugate corner elements at row-col intersection
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A( KP, KK ) = CONJG( A( KP, KK ) )
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* (4) Swap diagonal elements at row-col intersection
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R1 = REAL( A( KK, KK ) )
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@ -834,7 +834,7 @@
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A( J, K ) = CONJG( A( P, J ) )
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A( P, J ) = T
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44 CONTINUE
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* (3) Swap and conjugate corner elements at row-col interserction
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* (3) Swap and conjugate corner elements at row-col intersection
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A( P, K ) = CONJG( A( P, K ) )
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* (4) Swap diagonal elements at row-col intersection
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R1 = REAL( A( K, K ) )
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@ -862,7 +862,7 @@
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A( J, KK ) = CONJG( A( KP, J ) )
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A( KP, J ) = T
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45 CONTINUE
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* (3) Swap and conjugate corner elements at row-col interserction
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* (3) Swap and conjugate corner elements at row-col intersection
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A( KP, KK ) = CONJG( A( KP, KK ) )
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* (4) Swap diagonal elements at row-col intersection
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R1 = REAL( A( KK, KK ) )
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@ -420,7 +420,7 @@
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A( J, K ) = CONJG( A( P, J ) )
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A( P, J ) = T
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14 CONTINUE
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* (3) Swap and conjugate corner elements at row-col interserction
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* (3) Swap and conjugate corner elements at row-col intersection
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A( P, K ) = CONJG( A( P, K ) )
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* (4) Swap diagonal elements at row-col intersection
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R1 = REAL( A( K, K ) )
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@ -441,7 +441,7 @@
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A( J, KK ) = CONJG( A( KP, J ) )
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A( KP, J ) = T
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15 CONTINUE
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* (3) Swap and conjugate corner elements at row-col interserction
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* (3) Swap and conjugate corner elements at row-col intersection
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A( KP, KK ) = CONJG( A( KP, KK ) )
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* (4) Swap diagonal elements at row-col intersection
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R1 = REAL( A( KK, KK ) )
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@ -733,7 +733,7 @@
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A( J, K ) = CONJG( A( P, J ) )
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A( P, J ) = T
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44 CONTINUE
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* (3) Swap and conjugate corner elements at row-col interserction
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* (3) Swap and conjugate corner elements at row-col intersection
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A( P, K ) = CONJG( A( P, K ) )
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* (4) Swap diagonal elements at row-col intersection
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R1 = REAL( A( K, K ) )
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@ -754,7 +754,7 @@
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A( J, KK ) = CONJG( A( KP, J ) )
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A( KP, J ) = T
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45 CONTINUE
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* (3) Swap and conjugate corner elements at row-col interserction
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* (3) Swap and conjugate corner elements at row-col intersection
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A( KP, KK ) = CONJG( A( KP, KK ) )
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* (4) Swap diagonal elements at row-col intersection
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R1 = REAL( A( KK, KK ) )
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@ -74,7 +74,7 @@
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*>
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*> On exit, the tridiagonal matrix is stored in the diagonals
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*> and the subdiagonals of A just below (or above) the diagonals,
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*> and L is stored below (or above) the subdiaonals, when UPLO
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*> and L is stored below (or above) the subdiagonals, when UPLO
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*> is 'L' (or 'U').
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*> \endverbatim
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*>
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@ -75,7 +75,7 @@
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*> triangular part of the matrix A, and the strictly upper
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*> triangular part of A is not referenced.
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*>
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*> On exit, L is stored below (or above) the subdiaonal blocks,
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*> On exit, L is stored below (or above) the subdiagonal blocks,
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*> when UPLO is 'L' (or 'U').
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*> \endverbatim
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*>
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@ -18,7 +18,7 @@
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* Definition:
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* ===========
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*
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* SUBROUTINE CLA_GBRFSX_EXTENDED ( PREC_TYPE, TRANS_TYPE, N, KL, KU,
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* SUBROUTINE CLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU,
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* NRHS, AB, LDAB, AFB, LDAFB, IPIV,
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* COLEQU, C, B, LDB, Y, LDY,
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* BERR_OUT, N_NORMS, ERR_BNDS_NORM,
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*> \ingroup complexGBcomputational
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*
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* =====================================================================
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SUBROUTINE CLA_GBRFSX_EXTENDED ( PREC_TYPE, TRANS_TYPE, N, KL, KU,
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SUBROUTINE CLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU,
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$ NRHS, AB, LDAB, AFB, LDAFB, IPIV,
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$ COLEQU, C, B, LDB, Y, LDY,
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$ BERR_OUT, N_NORMS, ERR_BNDS_NORM,
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@ -651,7 +651,7 @@
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PREVNORMDX = NORMDX
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PREV_DZ_Z = DZ_Z
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*
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* Update soluton.
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* Update solution.
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*
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IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
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CALL CAXPY( N, (1.0E+0,0.0E+0), DY, 1, Y(1,J), 1 )
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@ -637,7 +637,7 @@
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PREVNORMDX = NORMDX
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PREV_DZ_Z = DZ_Z
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*
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* Update soluton.
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* Update solution.
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*
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IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
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CALL CAXPY( N, (1.0E+0,0.0E+0), DY, 1, Y(1,J), 1 )
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@ -654,7 +654,7 @@
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PREVNORMDX = NORMDX
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PREV_DZ_Z = DZ_Z
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*
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* Update soluton.
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* Update solution.
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*
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IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
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CALL CAXPY( N, CMPLX(1.0), DY, 1, Y(1,J), 1 )
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PREVNORMDX = NORMDX
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PREV_DZ_Z = DZ_Z
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*
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* Update soluton.
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* Update solution.
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*
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IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
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CALL CAXPY( N, CMPLX(1.0), DY, 1, Y(1,J), 1 )
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PREVNORMDX = NORMDX
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PREV_DZ_Z = DZ_Z
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*
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* Update soluton.
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* Update solution.
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*
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IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
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CALL CAXPY( N, CMPLX(1.0), DY, 1, Y(1,J), 1 )
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RETURN
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END IF
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*
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* Prepare the INDXQ sorting premutation.
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* Prepare the INDXQ sorting permutation.
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*
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N1 = K
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N2 = N - K
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*> Anal., 29(2006), pp. 199--227.
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*>
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*> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift,
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*> multipole rational QZ method with agressive early deflation"
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*> multipole rational QZ method with aggressive early deflation"
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*> \endverbatim
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*
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* Arguments:
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CHARACTER :: JBCMPZ*3
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* External Functions
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EXTERNAL :: XERBLA, CHGEQZ, CLAQZ2, CLAQZ3, CLASET, SLABAD,
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EXTERNAL :: XERBLA, CHGEQZ, CLAQZ2, CLAQZ3, CLASET,
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$ CLARTG, CROT
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REAL, EXTERNAL :: SLAMCH, CLANHS
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LOGICAL, EXTERNAL :: LSAME
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* Get machine constants
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SAFMIN = SLAMCH( 'SAFE MINIMUM' )
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SAFMAX = ONE/SAFMIN
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CALL SLABAD( SAFMIN, SAFMAX )
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ULP = SLAMCH( 'PRECISION' )
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SMLNUM = SAFMIN*( REAL( N )/ULP )
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DO WHILE ( K.GE.ISTART2 )
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IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
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* A diagonal element of B is negligable, move it
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* A diagonal element of B is negligible, move it
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* to the top and deflate it
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DO K2 = K, ISTART2+1, -1
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@ -452,7 +452,7 @@
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IF( LNOTIDENT ) THEN
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*
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* col2_(2) Compute W2: = (V1**H) * W2 = (A1**H) * W2,
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* V1 is not an identy matrix, but unit lower-triangular
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* V1 is not an identity matrix, but unit lower-triangular
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* V1 stored in A1 (diagonal ones are not stored).
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*
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*
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BM = RHS( J ) - CONE
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SPLUS = ONE
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*
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* Lockahead for L- part RHS(1:N-1) = +-1
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* Look-ahead for L- part RHS(1:N-1) = +-1
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* SPLUS and SMIN computed more efficiently than in BSOLVE[1].
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*
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SPLUS = SPLUS + REAL( CDOTC( N-J, Z( J+1, J ), 1, Z( J+1,
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* Prepare the linear update to be executed with GEMM.
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* For each column, compute a consistent scaling, a
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* scaling factor to survive the linear update, and
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* rescale the column segments, if necesssary. Then
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* rescale the column segments, if necessary. Then
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* the linear update is safely executed.
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*
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DO KK = 1, K2-K1
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*> CSYTRF provided on entry in parameter A into the factorization
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*> output format used in CSYTRF_RK (or CSYTRF_BK) that is stored
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*> on exit in parameters A and E. It also converts in place details of
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*> the intechanges stored in IPIV from the format used in CSYTRF into
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*> the interchanges stored in IPIV from the format used in CSYTRF into
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*> the format used in CSYTRF_RK (or CSYTRF_BK).
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*>
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*> If parameter WAY = 'R':
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*> (or CSYTRF_BK) provided on entry in parameters A and E into
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*> the factorization output format used in CSYTRF that is stored
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*> on exit in parameter A. It also converts in place details of
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*> the intechanges stored in IPIV from the format used in CSYTRF_RK
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*> the interchanges stored in IPIV from the format used in CSYTRF_RK
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*> (or CSYTRF_BK) into the format used in CSYTRF.
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*>
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*> CSYCONVF can also convert in Hermitian matrix case, i.e. between
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END IF
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*
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* Convert IPIV
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* There is no interchnge of rows i and and IPIV(i),
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* There is no interchange of rows i and and IPIV(i),
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* so this should be reflected in IPIV format for
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* *SYTRF_RK ( or *SYTRF_BK)
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*
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END IF
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*
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* Convert IPIV
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* There is no interchnge of rows i and and IPIV(i),
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* There is no interchange of rows i and and IPIV(i),
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* so this should be reflected in IPIV format for
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* *SYTRF_RK ( or *SYTRF_BK)
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*
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*
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* Revert VALUE
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* Assign subdiagonal entries of D from array E to
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* subgiagonal entries of A.
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* subdiagonal entries of A.
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*
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I = 1
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DO WHILE ( I.LE.N-1 )
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*
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* Revert VALUE
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* Assign subdiagonal entries of D from array E to
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* subgiagonal entries of A.
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* subdiagonal entries of A.
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*
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I = 1
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DO WHILE ( I.LE.N-1 )
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@ -87,7 +87,7 @@
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*> triangular part of the matrix A, and the strictly upper
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*> triangular part of A is not referenced.
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*>
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*> On exit, L is stored below (or above) the subdiaonal blocks,
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*> On exit, L is stored below (or above) the subdiagonal blocks,
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*> when UPLO is 'L' (or 'U').
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*> \endverbatim
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*>
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@ -74,7 +74,7 @@
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*>
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*> On exit, the tridiagonal matrix is stored in the diagonals
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*> and the subdiagonals of A just below (or above) the diagonals,
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*> and L is stored below (or above) the subdiaonals, when UPLO
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*> and L is stored below (or above) the subdiagonals, when UPLO
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*> is 'L' (or 'U').
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*> \endverbatim
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*>
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@ -75,7 +75,7 @@
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*> triangular part of the matrix A, and the strictly upper
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*> triangular part of A is not referenced.
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*>
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*> On exit, L is stored below (or above) the subdiaonal blocks,
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*> On exit, L is stored below (or above) the subdiagonal blocks,
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*> when UPLO is 'L' (or 'U').
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*> \endverbatim
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*>
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*>
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*> The Schur form T is reordered by a unitary similarity transformation
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*> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
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*> postmultplying it with Z.
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*> postmultiplying it with Z.
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*> \endverbatim
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*
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* Arguments:
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*>\verbatim
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*>
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*> CUNBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
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*> matrix X with orthonomal columns:
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*> matrix X with orthonormal columns:
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*>
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*> [ B11 ]
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*> [ X11 ] [ P1 | ] [ 0 ]
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@ -37,7 +37,7 @@
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*>\verbatim
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*>
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*> CUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
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*> matrix X with orthonomal columns:
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*> matrix X with orthonormal columns:
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*>
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*> [ B11 ]
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*> [ X11 ] [ P1 | ] [ 0 ]
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@ -37,7 +37,7 @@
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*>\verbatim
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*>
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*> CUNBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
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*> matrix X with orthonomal columns:
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*> matrix X with orthonormal columns:
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*>
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*> [ B11 ]
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*> [ X11 ] [ P1 | ] [ 0 ]
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|||
*>\verbatim
|
||||
*>
|
||||
*> CUNBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -45,7 +45,7 @@
|
|||
*>
|
||||
*> Given an upper bidiagonal B with diagonal D = [ d_1 d_2 ... d_N ]
|
||||
*> and superdiagonal E = [ e_1 e_2 ... e_N-1 ], DBDSVDX computes the
|
||||
*> singular value decompositon of B through the eigenvalues and
|
||||
*> singular value decomposition of B through the eigenvalues and
|
||||
*> eigenvectors of the N*2-by-N*2 tridiagonal matrix
|
||||
*>
|
||||
*> | 0 d_1 |
|
||||
|
|
|
@ -253,7 +253,7 @@
|
|||
*> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
|
||||
*> the right singular vectors;
|
||||
*> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
|
||||
*> then V is used as workspace if the pprocedure
|
||||
*> then V is used as workspace if the procedure
|
||||
*> replaces A with A^t. In that case, [U] is computed
|
||||
*> in V as right singular vectors of A^t and then
|
||||
*> copied back to the U array. This 'W' option is just
|
||||
|
|
|
@ -365,7 +365,7 @@
|
|||
*> an optimal implementation would do all necessary scaling before calling
|
||||
*> CGESVD and the scaling in CGESVD can be switched off.
|
||||
*> 3. Other comments related to code optimization are given in comments in the
|
||||
*> code, enlosed in [[double brackets]].
|
||||
*> code, enclosed in [[double brackets]].
|
||||
*> \endverbatim
|
||||
*
|
||||
*> \par Bugs, examples and comments
|
||||
|
|
|
@ -52,10 +52,10 @@
|
|||
*> Specifies whether the output from this procedure is used
|
||||
*> to compute the matrix V:
|
||||
*> = 'V': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the N-by-N array V.
|
||||
*> by postmultiplying the N-by-N array V.
|
||||
*> (See the description of V.)
|
||||
*> = 'A': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the MV-by-N array V.
|
||||
*> by postmultiplying the MV-by-N array V.
|
||||
*> (See the descriptions of MV and V.)
|
||||
*> = 'N': the Jacobi rotations are not accumulated.
|
||||
*> \endverbatim
|
||||
|
|
|
@ -75,10 +75,10 @@
|
|||
*> Specifies whether the output from this procedure is used
|
||||
*> to compute the matrix V:
|
||||
*> = 'V': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the N-by-N array V.
|
||||
*> by postmultiplying the N-by-N array V.
|
||||
*> (See the description of V.)
|
||||
*> = 'A': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the MV-by-N array V.
|
||||
*> by postmultiplying the MV-by-N array V.
|
||||
*> (See the descriptions of MV and V.)
|
||||
*> = 'N': the Jacobi rotations are not accumulated.
|
||||
*> \endverbatim
|
||||
|
|
|
@ -645,7 +645,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
|
||||
CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -625,7 +625,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
|
||||
CALL DAXPY( N, 1.0D+0, DY, 1, Y( 1, J ), 1 )
|
||||
|
|
|
@ -617,7 +617,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
|
||||
CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -647,7 +647,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
|
||||
CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -102,7 +102,7 @@
|
|||
*> Anal., 29(2006), pp. 199--227.
|
||||
*>
|
||||
*> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift,
|
||||
*> multipole rational QZ method with agressive early deflation"
|
||||
*> multipole rational QZ method with aggressive early deflation"
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
|
@ -332,7 +332,7 @@
|
|||
CHARACTER :: JBCMPZ*3
|
||||
|
||||
* External Functions
|
||||
EXTERNAL :: XERBLA, DHGEQZ, DLASET, DLAQZ3, DLAQZ4, DLABAD,
|
||||
EXTERNAL :: XERBLA, DHGEQZ, DLASET, DLAQZ3, DLAQZ4,
|
||||
$ DLARTG, DROT
|
||||
DOUBLE PRECISION, EXTERNAL :: DLAMCH, DLANHS
|
||||
LOGICAL, EXTERNAL :: LSAME
|
||||
|
@ -482,7 +482,6 @@
|
|||
* Get machine constants
|
||||
SAFMIN = DLAMCH( 'SAFE MINIMUM' )
|
||||
SAFMAX = ONE/SAFMIN
|
||||
CALL DLABAD( SAFMIN, SAFMAX )
|
||||
ULP = DLAMCH( 'PRECISION' )
|
||||
SMLNUM = SAFMIN*( DBLE( N )/ULP )
|
||||
|
||||
|
@ -567,7 +566,7 @@
|
|||
DO WHILE ( K.GE.ISTART2 )
|
||||
|
||||
IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
|
||||
* A diagonal element of B is negligable, move it
|
||||
* A diagonal element of B is negligible, move it
|
||||
* to the top and deflate it
|
||||
|
||||
DO K2 = K, ISTART2+1, -1
|
||||
|
|
|
@ -451,7 +451,7 @@
|
|||
IF( LNOTIDENT ) THEN
|
||||
*
|
||||
* col2_(2) Compute W2: = (V1**T) * W2 = (A1**T) * W2,
|
||||
* V1 is not an identy matrix, but unit lower-triangular
|
||||
* V1 is not an identity matrix, but unit lower-triangular
|
||||
* V1 stored in A1 (diagonal ones are not stored).
|
||||
*
|
||||
*
|
||||
|
|
|
@ -574,7 +574,7 @@
|
|||
* Prepare the linear update to be executed with GEMM.
|
||||
* For each column, compute a consistent scaling, a
|
||||
* scaling factor to survive the linear update, and
|
||||
* rescale the column segments, if necesssary. Then
|
||||
* rescale the column segments, if necessary. Then
|
||||
* the linear update is safely executed.
|
||||
*
|
||||
DO KK = 1, K2-K1
|
||||
|
|
|
@ -37,7 +37,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> DORBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -37,7 +37,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> DORBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -37,7 +37,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> DORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -38,7 +38,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> DORBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -39,7 +39,7 @@
|
|||
*> DSYTRF provided on entry in parameter A into the factorization
|
||||
*> output format used in DSYTRF_RK (or DSYTRF_BK) that is stored
|
||||
*> on exit in parameters A and E. It also converts in place details of
|
||||
*> the intechanges stored in IPIV from the format used in DSYTRF into
|
||||
*> the interchanges stored in IPIV from the format used in DSYTRF into
|
||||
*> the format used in DSYTRF_RK (or DSYTRF_BK).
|
||||
*>
|
||||
*> If parameter WAY = 'R':
|
||||
|
@ -48,7 +48,7 @@
|
|||
*> (or DSYTRF_BK) provided on entry in parameters A and E into
|
||||
*> the factorization output format used in DSYTRF that is stored
|
||||
*> on exit in parameter A. It also converts in place details of
|
||||
*> the intechanges stored in IPIV from the format used in DSYTRF_RK
|
||||
*> the interchanges stored in IPIV from the format used in DSYTRF_RK
|
||||
*> (or DSYTRF_BK) into the format used in DSYTRF.
|
||||
*> \endverbatim
|
||||
*
|
||||
|
@ -322,7 +322,7 @@
|
|||
END IF
|
||||
*
|
||||
* Convert IPIV
|
||||
* There is no interchnge of rows i and and IPIV(i),
|
||||
* There is no interchange of rows i and and IPIV(i),
|
||||
* so this should be reflected in IPIV format for
|
||||
* *SYTRF_RK ( or *SYTRF_BK)
|
||||
*
|
||||
|
@ -466,7 +466,7 @@
|
|||
END IF
|
||||
*
|
||||
* Convert IPIV
|
||||
* There is no interchnge of rows i and and IPIV(i),
|
||||
* There is no interchange of rows i and and IPIV(i),
|
||||
* so this should be reflected in IPIV format for
|
||||
* *SYTRF_RK ( or *SYTRF_BK)
|
||||
*
|
||||
|
@ -532,7 +532,7 @@
|
|||
*
|
||||
* Revert VALUE
|
||||
* Assign subdiagonal entries of D from array E to
|
||||
* subgiagonal entries of A.
|
||||
* subdiagonal entries of A.
|
||||
*
|
||||
I = 1
|
||||
DO WHILE ( I.LE.N-1 )
|
||||
|
|
|
@ -517,7 +517,7 @@
|
|||
*
|
||||
* Revert VALUE
|
||||
* Assign subdiagonal entries of D from array E to
|
||||
* subgiagonal entries of A.
|
||||
* subdiagonal entries of A.
|
||||
*
|
||||
I = 1
|
||||
DO WHILE ( I.LE.N-1 )
|
||||
|
|
|
@ -89,7 +89,7 @@
|
|||
*> triangular part of the matrix A, and the strictly upper
|
||||
*> triangular part of A is not referenced.
|
||||
*>
|
||||
*> On exit, L is stored below (or above) the subdiaonal blocks,
|
||||
*> On exit, L is stored below (or above) the subdiagonal blocks,
|
||||
*> when UPLO is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -74,7 +74,7 @@
|
|||
*>
|
||||
*> On exit, the tridiagonal matrix is stored in the diagonals
|
||||
*> and the subdiagonals of A just below (or above) the diagonals,
|
||||
*> and L is stored below (or above) the subdiaonals, when UPLO
|
||||
*> and L is stored below (or above) the subdiagonals, when UPLO
|
||||
*> is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -75,7 +75,7 @@
|
|||
*> triangular part of the matrix A, and the strictly upper
|
||||
*> triangular part of A is not referenced.
|
||||
*>
|
||||
*> On exit, L is stored below (or above) the subdiaonal blocks,
|
||||
*> On exit, L is stored below (or above) the subdiagonal blocks,
|
||||
*> when UPLO is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -45,7 +45,7 @@
|
|||
*>
|
||||
*> Given an upper bidiagonal B with diagonal D = [ d_1 d_2 ... d_N ]
|
||||
*> and superdiagonal E = [ e_1 e_2 ... e_N-1 ], SBDSVDX computes the
|
||||
*> singular value decompositon of B through the eigenvalues and
|
||||
*> singular value decomposition of B through the eigenvalues and
|
||||
*> eigenvectors of the N*2-by-N*2 tridiagonal matrix
|
||||
*>
|
||||
*> | 0 d_1 |
|
||||
|
|
|
@ -253,7 +253,7 @@
|
|||
*> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
|
||||
*> the right singular vectors;
|
||||
*> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
|
||||
*> then V is used as workspace if the pprocedure
|
||||
*> then V is used as workspace if the procedure
|
||||
*> replaces A with A^t. In that case, [U] is computed
|
||||
*> in V as right singular vectors of A^t and then
|
||||
*> copied back to the U array. This 'W' option is just
|
||||
|
|
|
@ -365,7 +365,7 @@
|
|||
*> an optimal implementation would do all necessary scaling before calling
|
||||
*> CGESVD and the scaling in CGESVD can be switched off.
|
||||
*> 3. Other comments related to code optimization are given in comments in the
|
||||
*> code, enlosed in [[double brackets]].
|
||||
*> code, enclosed in [[double brackets]].
|
||||
*> \endverbatim
|
||||
*
|
||||
*> \par Bugs, examples and comments
|
||||
|
|
|
@ -52,10 +52,10 @@
|
|||
*> Specifies whether the output from this procedure is used
|
||||
*> to compute the matrix V:
|
||||
*> = 'V': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the N-by-N array V.
|
||||
*> by postmultiplying the N-by-N array V.
|
||||
*> (See the description of V.)
|
||||
*> = 'A': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the MV-by-N array V.
|
||||
*> by postmultiplying the MV-by-N array V.
|
||||
*> (See the descriptions of MV and V.)
|
||||
*> = 'N': the Jacobi rotations are not accumulated.
|
||||
*> \endverbatim
|
||||
|
|
|
@ -75,10 +75,10 @@
|
|||
*> Specifies whether the output from this procedure is used
|
||||
*> to compute the matrix V:
|
||||
*> = 'V': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the N-by-N array V.
|
||||
*> by postmultiplying the N-by-N array V.
|
||||
*> (See the description of V.)
|
||||
*> = 'A': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the MV-by-N array V.
|
||||
*> by postmultiplying the MV-by-N array V.
|
||||
*> (See the descriptions of MV and V.)
|
||||
*> = 'N': the Jacobi rotations are not accumulated.
|
||||
*> \endverbatim
|
||||
|
|
|
@ -644,7 +644,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
|
||||
CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -628,7 +628,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
|
||||
CALL SAXPY( N, 1.0, DY, 1, Y( 1, J ), 1 )
|
||||
|
|
|
@ -617,7 +617,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
|
||||
CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -647,7 +647,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
|
||||
CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -100,7 +100,7 @@
|
|||
*> Anal., 29(2006), pp. 199--227.
|
||||
*>
|
||||
*> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift,
|
||||
*> multipole rational QZ method with agressive early deflation"
|
||||
*> multipole rational QZ method with aggressive early deflation"
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
|
@ -329,7 +329,7 @@
|
|||
CHARACTER :: JBCMPZ*3
|
||||
|
||||
* External Functions
|
||||
EXTERNAL :: XERBLA, SHGEQZ, SLAQZ3, SLAQZ4, SLASET, SLABAD,
|
||||
EXTERNAL :: XERBLA, SHGEQZ, SLAQZ3, SLAQZ4, SLASET,
|
||||
$ SLARTG, SROT
|
||||
REAL, EXTERNAL :: SLAMCH, SLANHS
|
||||
LOGICAL, EXTERNAL :: LSAME
|
||||
|
@ -479,7 +479,6 @@
|
|||
* Get machine constants
|
||||
SAFMIN = SLAMCH( 'SAFE MINIMUM' )
|
||||
SAFMAX = ONE/SAFMIN
|
||||
CALL SLABAD( SAFMIN, SAFMAX )
|
||||
ULP = SLAMCH( 'PRECISION' )
|
||||
SMLNUM = SAFMIN*( REAL( N )/ULP )
|
||||
|
||||
|
@ -564,7 +563,7 @@
|
|||
DO WHILE ( K.GE.ISTART2 )
|
||||
|
||||
IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
|
||||
* A diagonal element of B is negligable, move it
|
||||
* A diagonal element of B is negligible, move it
|
||||
* to the top and deflate it
|
||||
|
||||
DO K2 = K, ISTART2+1, -1
|
||||
|
|
|
@ -451,7 +451,7 @@
|
|||
IF( LNOTIDENT ) THEN
|
||||
*
|
||||
* col2_(2) Compute W2: = (V1**T) * W2 = (A1**T) * W2,
|
||||
* V1 is not an identy matrix, but unit lower-triangular
|
||||
* V1 is not an identity matrix, but unit lower-triangular
|
||||
* V1 stored in A1 (diagonal ones are not stored).
|
||||
*
|
||||
*
|
||||
|
|
|
@ -574,7 +574,7 @@
|
|||
* Prepare the linear update to be executed with GEMM.
|
||||
* For each column, compute a consistent scaling, a
|
||||
* scaling factor to survive the linear update, and
|
||||
* rescale the column segments, if necesssary. Then
|
||||
* rescale the column segments, if necessary. Then
|
||||
* the linear update is safely executed.
|
||||
*
|
||||
DO KK = 1, K2-K1
|
||||
|
|
|
@ -37,7 +37,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> SORBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -37,7 +37,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> SORBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -37,7 +37,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> SORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -38,7 +38,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> SORBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -39,7 +39,7 @@
|
|||
*> SSYTRF provided on entry in parameter A into the factorization
|
||||
*> output format used in SSYTRF_RK (or SSYTRF_BK) that is stored
|
||||
*> on exit in parameters A and E. It also converts in place details of
|
||||
*> the intechanges stored in IPIV from the format used in SSYTRF into
|
||||
*> the interchanges stored in IPIV from the format used in SSYTRF into
|
||||
*> the format used in SSYTRF_RK (or SSYTRF_BK).
|
||||
*>
|
||||
*> If parameter WAY = 'R':
|
||||
|
@ -48,7 +48,7 @@
|
|||
*> (or SSYTRF_BK) provided on entry in parameters A and E into
|
||||
*> the factorization output format used in SSYTRF that is stored
|
||||
*> on exit in parameter A. It also converts in place details of
|
||||
*> the intechanges stored in IPIV from the format used in SSYTRF_RK
|
||||
*> the interchanges stored in IPIV from the format used in SSYTRF_RK
|
||||
*> (or SSYTRF_BK) into the format used in SSYTRF.
|
||||
*> \endverbatim
|
||||
*
|
||||
|
@ -322,7 +322,7 @@
|
|||
END IF
|
||||
*
|
||||
* Convert IPIV
|
||||
* There is no interchnge of rows i and and IPIV(i),
|
||||
* There is no interchange of rows i and and IPIV(i),
|
||||
* so this should be reflected in IPIV format for
|
||||
* *SYTRF_RK ( or *SYTRF_BK)
|
||||
*
|
||||
|
@ -466,7 +466,7 @@
|
|||
END IF
|
||||
*
|
||||
* Convert IPIV
|
||||
* There is no interchnge of rows i and and IPIV(i),
|
||||
* There is no interchange of rows i and and IPIV(i),
|
||||
* so this should be reflected in IPIV format for
|
||||
* *SYTRF_RK ( or *SYTRF_BK)
|
||||
*
|
||||
|
@ -532,7 +532,7 @@
|
|||
*
|
||||
* Revert VALUE
|
||||
* Assign subdiagonal entries of D from array E to
|
||||
* subgiagonal entries of A.
|
||||
* subdiagonal entries of A.
|
||||
*
|
||||
I = 1
|
||||
DO WHILE ( I.LE.N-1 )
|
||||
|
|
|
@ -517,7 +517,7 @@
|
|||
*
|
||||
* Revert VALUE
|
||||
* Assign subdiagonal entries of D from array E to
|
||||
* subgiagonal entries of A.
|
||||
* subdiagonal entries of A.
|
||||
*
|
||||
I = 1
|
||||
DO WHILE ( I.LE.N-1 )
|
||||
|
|
|
@ -88,7 +88,7 @@
|
|||
*> triangular part of the matrix A, and the strictly upper
|
||||
*> triangular part of A is not referenced.
|
||||
*>
|
||||
*> On exit, L is stored below (or above) the subdiaonal blocks,
|
||||
*> On exit, L is stored below (or above) the subdiagonal blocks,
|
||||
*> when UPLO is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -74,7 +74,7 @@
|
|||
*>
|
||||
*> On exit, the tridiagonal matrix is stored in the diagonals
|
||||
*> and the subdiagonals of A just below (or above) the diagonals,
|
||||
*> and L is stored below (or above) the subdiaonals, when UPLO
|
||||
*> and L is stored below (or above) the subdiagonals, when UPLO
|
||||
*> is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -75,7 +75,7 @@
|
|||
*> triangular part of the matrix A, and the strictly upper
|
||||
*> triangular part of A is not referenced.
|
||||
*>
|
||||
*> On exit, L is stored below (or above) the subdiaonal blocks,
|
||||
*> On exit, L is stored below (or above) the subdiagonal blocks,
|
||||
*> when UPLO is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -252,7 +252,7 @@
|
|||
*> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
|
||||
*> the right singular vectors;
|
||||
*> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
|
||||
*> then V is used as workspace if the pprocedure
|
||||
*> then V is used as workspace if the procedure
|
||||
*> replaces A with A^*. In that case, [U] is computed
|
||||
*> in V as right singular vectors of A^* and then
|
||||
*> copied back to the U array. This 'W' option is just
|
||||
|
|
|
@ -363,7 +363,7 @@
|
|||
*> an optimal implementation would do all necessary scaling before calling
|
||||
*> CGESVD and the scaling in CGESVD can be switched off.
|
||||
*> 3. Other comments related to code optimization are given in comments in the
|
||||
*> code, enlosed in [[double brackets]].
|
||||
*> code, enclosed in [[double brackets]].
|
||||
*> \endverbatim
|
||||
*
|
||||
*> \par Bugs, examples and comments
|
||||
|
|
|
@ -52,10 +52,10 @@
|
|||
*> Specifies whether the output from this procedure is used
|
||||
*> to compute the matrix V:
|
||||
*> = 'V': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the N-by-N array V.
|
||||
*> by postmultiplying the N-by-N array V.
|
||||
*> (See the description of V.)
|
||||
*> = 'A': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the MV-by-N array V.
|
||||
*> by postmultiplying the MV-by-N array V.
|
||||
*> (See the descriptions of MV and V.)
|
||||
*> = 'N': the Jacobi rotations are not accumulated.
|
||||
*> \endverbatim
|
||||
|
|
|
@ -75,10 +75,10 @@
|
|||
*> Specifies whether the output from this procedure is used
|
||||
*> to compute the matrix V:
|
||||
*> = 'V': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the N-by-N array V.
|
||||
*> by postmultiplying the N-by-N array V.
|
||||
*> (See the description of V.)
|
||||
*> = 'A': the product of the Jacobi rotations is accumulated
|
||||
*> by postmulyiplying the MV-by-N array V.
|
||||
*> by postmultiplying the MV-by-N array V.
|
||||
*> (See the descriptions of MV and V.)
|
||||
*> = 'N': the Jacobi rotations are not accumulated.
|
||||
*> \endverbatim
|
||||
|
|
|
@ -88,7 +88,7 @@
|
|||
*> triangular part of the matrix A, and the strictly upper
|
||||
*> triangular part of A is not referenced.
|
||||
*>
|
||||
*> On exit, L is stored below (or above) the subdiaonal blocks,
|
||||
*> On exit, L is stored below (or above) the subdiagonal blocks,
|
||||
*> when UPLO is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -480,7 +480,7 @@
|
|||
A( J, K ) = DCONJG( A( P, J ) )
|
||||
A( P, J ) = T
|
||||
14 CONTINUE
|
||||
* (3) Swap and conjugate corner elements at row-col interserction
|
||||
* (3) Swap and conjugate corner elements at row-col intersection
|
||||
A( P, K ) = DCONJG( A( P, K ) )
|
||||
* (4) Swap diagonal elements at row-col intersection
|
||||
R1 = DBLE( A( K, K ) )
|
||||
|
@ -508,7 +508,7 @@
|
|||
A( J, KK ) = DCONJG( A( KP, J ) )
|
||||
A( KP, J ) = T
|
||||
15 CONTINUE
|
||||
* (3) Swap and conjugate corner elements at row-col interserction
|
||||
* (3) Swap and conjugate corner elements at row-col intersection
|
||||
A( KP, KK ) = DCONJG( A( KP, KK ) )
|
||||
* (4) Swap diagonal elements at row-col intersection
|
||||
R1 = DBLE( A( KK, KK ) )
|
||||
|
@ -834,7 +834,7 @@
|
|||
A( J, K ) = DCONJG( A( P, J ) )
|
||||
A( P, J ) = T
|
||||
44 CONTINUE
|
||||
* (3) Swap and conjugate corner elements at row-col interserction
|
||||
* (3) Swap and conjugate corner elements at row-col intersection
|
||||
A( P, K ) = DCONJG( A( P, K ) )
|
||||
* (4) Swap diagonal elements at row-col intersection
|
||||
R1 = DBLE( A( K, K ) )
|
||||
|
@ -862,7 +862,7 @@
|
|||
A( J, KK ) = DCONJG( A( KP, J ) )
|
||||
A( KP, J ) = T
|
||||
45 CONTINUE
|
||||
* (3) Swap and conjugate corner elements at row-col interserction
|
||||
* (3) Swap and conjugate corner elements at row-col intersection
|
||||
A( KP, KK ) = DCONJG( A( KP, KK ) )
|
||||
* (4) Swap diagonal elements at row-col intersection
|
||||
R1 = DBLE( A( KK, KK ) )
|
||||
|
|
|
@ -420,7 +420,7 @@
|
|||
A( J, K ) = DCONJG( A( P, J ) )
|
||||
A( P, J ) = T
|
||||
14 CONTINUE
|
||||
* (3) Swap and conjugate corner elements at row-col interserction
|
||||
* (3) Swap and conjugate corner elements at row-col intersection
|
||||
A( P, K ) = DCONJG( A( P, K ) )
|
||||
* (4) Swap diagonal elements at row-col intersection
|
||||
R1 = DBLE( A( K, K ) )
|
||||
|
@ -441,7 +441,7 @@
|
|||
A( J, KK ) = DCONJG( A( KP, J ) )
|
||||
A( KP, J ) = T
|
||||
15 CONTINUE
|
||||
* (3) Swap and conjugate corner elements at row-col interserction
|
||||
* (3) Swap and conjugate corner elements at row-col intersection
|
||||
A( KP, KK ) = DCONJG( A( KP, KK ) )
|
||||
* (4) Swap diagonal elements at row-col intersection
|
||||
R1 = DBLE( A( KK, KK ) )
|
||||
|
@ -733,7 +733,7 @@
|
|||
A( J, K ) = DCONJG( A( P, J ) )
|
||||
A( P, J ) = T
|
||||
44 CONTINUE
|
||||
* (3) Swap and conjugate corner elements at row-col interserction
|
||||
* (3) Swap and conjugate corner elements at row-col intersection
|
||||
A( P, K ) = DCONJG( A( P, K ) )
|
||||
* (4) Swap diagonal elements at row-col intersection
|
||||
R1 = DBLE( A( K, K ) )
|
||||
|
@ -754,7 +754,7 @@
|
|||
A( J, KK ) = DCONJG( A( KP, J ) )
|
||||
A( KP, J ) = T
|
||||
45 CONTINUE
|
||||
* (3) Swap and conjugate corner elements at row-col interserction
|
||||
* (3) Swap and conjugate corner elements at row-col intersection
|
||||
A( KP, KK ) = DCONJG( A( KP, KK ) )
|
||||
* (4) Swap diagonal elements at row-col intersection
|
||||
R1 = DBLE( A( KK, KK ) )
|
||||
|
|
|
@ -74,7 +74,7 @@
|
|||
*>
|
||||
*> On exit, the tridiagonal matrix is stored in the diagonals
|
||||
*> and the subdiagonals of A just below (or above) the diagonals,
|
||||
*> and L is stored below (or above) the subdiaonals, when UPLO
|
||||
*> and L is stored below (or above) the subdiagonals, when UPLO
|
||||
*> is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -75,7 +75,7 @@
|
|||
*> triangular part of the matrix A, and the strictly upper
|
||||
*> triangular part of A is not referenced.
|
||||
*>
|
||||
*> On exit, L is stored below (or above) the subdiaonal blocks,
|
||||
*> On exit, L is stored below (or above) the subdiagonal blocks,
|
||||
*> when UPLO is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -651,7 +651,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
|
||||
CALL ZAXPY( N, (1.0D+0,0.0D+0), DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -636,7 +636,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
|
||||
CALL ZAXPY( N, (1.0D+0,0.0D+0), DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -655,7 +655,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
|
||||
CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -626,7 +626,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
|
||||
CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -655,7 +655,7 @@
|
|||
PREVNORMDX = NORMDX
|
||||
PREV_DZ_Z = DZ_Z
|
||||
*
|
||||
* Update soluton.
|
||||
* Update solution.
|
||||
*
|
||||
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
|
||||
CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 )
|
||||
|
|
|
@ -363,7 +363,7 @@
|
|||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Prepare the INDXQ sorting premutation.
|
||||
* Prepare the INDXQ sorting permutation.
|
||||
*
|
||||
N1 = K
|
||||
N2 = N - K
|
||||
|
|
|
@ -89,7 +89,7 @@
|
|||
*> Anal., 29(2006), pp. 199--227.
|
||||
*>
|
||||
*> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift,
|
||||
*> multipole rational QZ method with agressive early deflation"
|
||||
*> multipole rational QZ method with aggressive early deflation"
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
|
@ -312,7 +312,7 @@
|
|||
CHARACTER :: JBCMPZ*3
|
||||
|
||||
* External Functions
|
||||
EXTERNAL :: XERBLA, ZHGEQZ, ZLAQZ2, ZLAQZ3, ZLASET, DLABAD,
|
||||
EXTERNAL :: XERBLA, ZHGEQZ, ZLAQZ2, ZLAQZ3, ZLASET,
|
||||
$ ZLARTG, ZROT
|
||||
DOUBLE PRECISION, EXTERNAL :: DLAMCH, ZLANHS
|
||||
LOGICAL, EXTERNAL :: LSAME
|
||||
|
@ -464,7 +464,6 @@
|
|||
* Get machine constants
|
||||
SAFMIN = DLAMCH( 'SAFE MINIMUM' )
|
||||
SAFMAX = ONE/SAFMIN
|
||||
CALL DLABAD( SAFMIN, SAFMAX )
|
||||
ULP = DLAMCH( 'PRECISION' )
|
||||
SMLNUM = SAFMIN*( DBLE( N )/ULP )
|
||||
|
||||
|
@ -535,7 +534,7 @@
|
|||
DO WHILE ( K.GE.ISTART2 )
|
||||
|
||||
IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
|
||||
* A diagonal element of B is negligable, move it
|
||||
* A diagonal element of B is negligible, move it
|
||||
* to the top and deflate it
|
||||
|
||||
DO K2 = K, ISTART2+1, -1
|
||||
|
|
|
@ -452,7 +452,7 @@
|
|||
IF( LNOTIDENT ) THEN
|
||||
*
|
||||
* col2_(2) Compute W2: = (V1**H) * W2 = (A1**H) * W2,
|
||||
* V1 is not an identy matrix, but unit lower-triangular
|
||||
* V1 is not an identity matrix, but unit lower-triangular
|
||||
* V1 stored in A1 (diagonal ones are not stored).
|
||||
*
|
||||
*
|
||||
|
|
|
@ -227,7 +227,7 @@
|
|||
BM = RHS( J ) - CONE
|
||||
SPLUS = ONE
|
||||
*
|
||||
* Lockahead for L- part RHS(1:N-1) = +-1
|
||||
* Look-ahead for L- part RHS(1:N-1) = +-1
|
||||
* SPLUS and SMIN computed more efficiently than in BSOLVE[1].
|
||||
*
|
||||
SPLUS = SPLUS + DBLE( ZDOTC( N-J, Z( J+1, J ), 1, Z( J+1,
|
||||
|
|
|
@ -577,7 +577,7 @@
|
|||
* Prepare the linear update to be executed with GEMM.
|
||||
* For each column, compute a consistent scaling, a
|
||||
* scaling factor to survive the linear update, and
|
||||
* rescale the column segments, if necesssary. Then
|
||||
* rescale the column segments, if necessary. Then
|
||||
* the linear update is safely executed.
|
||||
*
|
||||
DO KK = 1, K2 - K1
|
||||
|
|
|
@ -39,7 +39,7 @@
|
|||
*> ZSYTRF provided on entry in parameter A into the factorization
|
||||
*> output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored
|
||||
*> on exit in parameters A and E. It also converts in place details of
|
||||
*> the intechanges stored in IPIV from the format used in ZSYTRF into
|
||||
*> the interchanges stored in IPIV from the format used in ZSYTRF into
|
||||
*> the format used in ZSYTRF_RK (or ZSYTRF_BK).
|
||||
*>
|
||||
*> If parameter WAY = 'R':
|
||||
|
@ -48,7 +48,7 @@
|
|||
*> (or ZSYTRF_BK) provided on entry in parameters A and E into
|
||||
*> the factorization output format used in ZSYTRF that is stored
|
||||
*> on exit in parameter A. It also converts in place details of
|
||||
*> the intechanges stored in IPIV from the format used in ZSYTRF_RK
|
||||
*> the interchanges stored in IPIV from the format used in ZSYTRF_RK
|
||||
*> (or ZSYTRF_BK) into the format used in ZSYTRF.
|
||||
*>
|
||||
*> ZSYCONVF can also convert in Hermitian matrix case, i.e. between
|
||||
|
@ -325,7 +325,7 @@
|
|||
END IF
|
||||
*
|
||||
* Convert IPIV
|
||||
* There is no interchnge of rows i and and IPIV(i),
|
||||
* There is no interchange of rows i and and IPIV(i),
|
||||
* so this should be reflected in IPIV format for
|
||||
* *SYTRF_RK ( or *SYTRF_BK)
|
||||
*
|
||||
|
@ -469,7 +469,7 @@
|
|||
END IF
|
||||
*
|
||||
* Convert IPIV
|
||||
* There is no interchnge of rows i and and IPIV(i),
|
||||
* There is no interchange of rows i and and IPIV(i),
|
||||
* so this should be reflected in IPIV format for
|
||||
* *SYTRF_RK ( or *SYTRF_BK)
|
||||
*
|
||||
|
@ -535,7 +535,7 @@
|
|||
*
|
||||
* Revert VALUE
|
||||
* Assign subdiagonal entries of D from array E to
|
||||
* subgiagonal entries of A.
|
||||
* subdiagonal entries of A.
|
||||
*
|
||||
I = 1
|
||||
DO WHILE ( I.LE.N-1 )
|
||||
|
|
|
@ -520,7 +520,7 @@
|
|||
*
|
||||
* Revert VALUE
|
||||
* Assign subdiagonal entries of D from array E to
|
||||
* subgiagonal entries of A.
|
||||
* subdiagonal entries of A.
|
||||
*
|
||||
I = 1
|
||||
DO WHILE ( I.LE.N-1 )
|
||||
|
|
|
@ -87,7 +87,7 @@
|
|||
*> triangular part of the matrix A, and the strictly upper
|
||||
*> triangular part of A is not referenced.
|
||||
*>
|
||||
*> On exit, L is stored below (or above) the subdiaonal blocks,
|
||||
*> On exit, L is stored below (or above) the subdiagonal blocks,
|
||||
*> when UPLO is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -74,7 +74,7 @@
|
|||
*>
|
||||
*> On exit, the tridiagonal matrix is stored in the diagonals
|
||||
*> and the subdiagonals of A just below (or above) the diagonals,
|
||||
*> and L is stored below (or above) the subdiaonals, when UPLO
|
||||
*> and L is stored below (or above) the subdiagonals, when UPLO
|
||||
*> is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -75,7 +75,7 @@
|
|||
*> triangular part of the matrix A, and the strictly upper
|
||||
*> triangular part of A is not referenced.
|
||||
*>
|
||||
*> On exit, L is stored below (or above) the subdiaonal blocks,
|
||||
*> On exit, L is stored below (or above) the subdiagonal blocks,
|
||||
*> when UPLO is 'L' (or 'U').
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
|
|
@ -40,7 +40,7 @@
|
|||
*>
|
||||
*> The Schur form T is reordered by a unitary similarity transformation
|
||||
*> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
|
||||
*> postmultplying it with Z.
|
||||
*> postmultiplying it with Z.
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
|
|
|
@ -37,7 +37,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> ZUNBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -37,7 +37,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> ZUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -37,7 +37,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> ZUNBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
|
@ -38,7 +38,7 @@
|
|||
*>\verbatim
|
||||
*>
|
||||
*> ZUNBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
|
||||
*> matrix X with orthonomal columns:
|
||||
*> matrix X with orthonormal columns:
|
||||
*>
|
||||
*> [ B11 ]
|
||||
*> [ X11 ] [ P1 | ] [ 0 ]
|
||||
|
|
Loading…
Reference in New Issue