version 1.6, 2011/07/22 07:38:12
|
version 1.16, 2018/05/29 07:18:10
|
Line 1
|
Line 1
|
SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, |
*> \brief \b DTFSM solves a matrix equation (one operand is a triangular matrix in RFP format). |
$ B, LDB ) |
* |
|
* =========== DOCUMENTATION =========== |
* |
* |
* -- LAPACK routine (version 3.3.1) -- |
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- |
*> \htmlonly |
* -- April 2011 -- |
*> Download DTFSM + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtfsm.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtfsm.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtfsm.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, |
|
* B, LDB ) |
|
* |
|
* .. Scalar Arguments .. |
|
* CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO |
|
* INTEGER LDB, M, N |
|
* DOUBLE PRECISION ALPHA |
|
* .. |
|
* .. Array Arguments .. |
|
* DOUBLE PRECISION A( 0: * ), B( 0: LDB-1, 0: * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> Level 3 BLAS like routine for A in RFP Format. |
|
*> |
|
*> DTFSM solves the matrix equation |
|
*> |
|
*> op( A )*X = alpha*B or X*op( A ) = alpha*B |
|
*> |
|
*> where alpha is a scalar, X and B are m by n matrices, A is a unit, or |
|
*> non-unit, upper or lower triangular matrix and op( A ) is one of |
|
*> |
|
*> op( A ) = A or op( A ) = A**T. |
|
*> |
|
*> A is in Rectangular Full Packed (RFP) Format. |
|
*> |
|
*> The matrix X is overwritten on B. |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
* |
* |
|
*> \param[in] TRANSR |
|
*> \verbatim |
|
*> TRANSR is CHARACTER*1 |
|
*> = 'N': The Normal Form of RFP A is stored; |
|
*> = 'T': The Transpose Form of RFP A is stored. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] SIDE |
|
*> \verbatim |
|
*> SIDE is CHARACTER*1 |
|
*> On entry, SIDE specifies whether op( A ) appears on the left |
|
*> or right of X as follows: |
|
*> |
|
*> SIDE = 'L' or 'l' op( A )*X = alpha*B. |
|
*> |
|
*> SIDE = 'R' or 'r' X*op( A ) = alpha*B. |
|
*> |
|
*> Unchanged on exit. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] UPLO |
|
*> \verbatim |
|
*> UPLO is CHARACTER*1 |
|
*> On entry, UPLO specifies whether the RFP matrix A came from |
|
*> an upper or lower triangular matrix as follows: |
|
*> UPLO = 'U' or 'u' RFP A came from an upper triangular matrix |
|
*> UPLO = 'L' or 'l' RFP A came from a lower triangular matrix |
|
*> |
|
*> Unchanged on exit. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] TRANS |
|
*> \verbatim |
|
*> TRANS is CHARACTER*1 |
|
*> On entry, TRANS specifies the form of op( A ) to be used |
|
*> in the matrix multiplication as follows: |
|
*> |
|
*> TRANS = 'N' or 'n' op( A ) = A. |
|
*> |
|
*> TRANS = 'T' or 't' op( A ) = A'. |
|
*> |
|
*> Unchanged on exit. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] DIAG |
|
*> \verbatim |
|
*> DIAG is CHARACTER*1 |
|
*> On entry, DIAG specifies whether or not RFP A is unit |
|
*> triangular as follows: |
|
*> |
|
*> DIAG = 'U' or 'u' A is assumed to be unit triangular. |
|
*> |
|
*> DIAG = 'N' or 'n' A is not assumed to be unit |
|
*> triangular. |
|
*> |
|
*> Unchanged on exit. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] M |
|
*> \verbatim |
|
*> M is INTEGER |
|
*> On entry, M specifies the number of rows of B. M must be at |
|
*> least zero. |
|
*> Unchanged on exit. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> On entry, N specifies the number of columns of B. N must be |
|
*> at least zero. |
|
*> Unchanged on exit. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] ALPHA |
|
*> \verbatim |
|
*> ALPHA is DOUBLE PRECISION |
|
*> On entry, ALPHA specifies the scalar alpha. When alpha is |
|
*> zero then A is not referenced and B need not be set before |
|
*> entry. |
|
*> Unchanged on exit. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] A |
|
*> \verbatim |
|
*> A is DOUBLE PRECISION array, dimension (NT) |
|
*> NT = N*(N+1)/2. On entry, the matrix A in RFP Format. |
|
*> RFP Format is described by TRANSR, UPLO and N as follows: |
|
*> If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; |
|
*> K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If |
|
*> TRANSR = 'T' then RFP is the transpose of RFP A as |
|
*> defined when TRANSR = 'N'. The contents of RFP A are defined |
|
*> by UPLO as follows: If UPLO = 'U' the RFP A contains the NT |
|
*> elements of upper packed A either in normal or |
|
*> transpose Format. If UPLO = 'L' the RFP A contains |
|
*> the NT elements of lower packed A either in normal or |
|
*> transpose Format. The LDA of RFP A is (N+1)/2 when |
|
*> TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is |
|
*> even and is N when is odd. |
|
*> See the Note below for more details. Unchanged on exit. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] B |
|
*> \verbatim |
|
*> B is DOUBLE PRECISION array, dimension (LDB,N) |
|
*> Before entry, the leading m by n part of the array B must |
|
*> contain the right-hand side matrix B, and on exit is |
|
*> overwritten by the solution matrix X. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDB |
|
*> \verbatim |
|
*> LDB is INTEGER |
|
*> On entry, LDB specifies the first dimension of B as declared |
|
*> in the calling (sub) program. LDB must be at least |
|
*> max( 1, m ). |
|
*> Unchanged on exit. |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \date December 2016 |
|
* |
|
*> \ingroup doubleOTHERcomputational |
|
* |
|
*> \par Further Details: |
|
* ===================== |
|
*> |
|
*> \verbatim |
|
*> |
|
*> We first consider Rectangular Full Packed (RFP) Format when N is |
|
*> even. We give an example where N = 6. |
|
*> |
|
*> AP is Upper AP is Lower |
|
*> |
|
*> 00 01 02 03 04 05 00 |
|
*> 11 12 13 14 15 10 11 |
|
*> 22 23 24 25 20 21 22 |
|
*> 33 34 35 30 31 32 33 |
|
*> 44 45 40 41 42 43 44 |
|
*> 55 50 51 52 53 54 55 |
|
*> |
|
*> |
|
*> Let TRANSR = 'N'. RFP holds AP as follows: |
|
*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last |
|
*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of |
|
*> the transpose of the first three columns of AP upper. |
|
*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first |
|
*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of |
|
*> the transpose of the last three columns of AP lower. |
|
*> This covers the case N even and TRANSR = 'N'. |
|
*> |
|
*> RFP A RFP A |
|
*> |
|
*> 03 04 05 33 43 53 |
|
*> 13 14 15 00 44 54 |
|
*> 23 24 25 10 11 55 |
|
*> 33 34 35 20 21 22 |
|
*> 00 44 45 30 31 32 |
|
*> 01 11 55 40 41 42 |
|
*> 02 12 22 50 51 52 |
|
*> |
|
*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the |
|
*> transpose of RFP A above. One therefore gets: |
|
*> |
|
*> |
|
*> RFP A RFP A |
|
*> |
|
*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 |
|
*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 |
|
*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 |
|
*> |
|
*> |
|
*> We then consider Rectangular Full Packed (RFP) Format when N is |
|
*> odd. We give an example where N = 5. |
|
*> |
|
*> AP is Upper AP is Lower |
|
*> |
|
*> 00 01 02 03 04 00 |
|
*> 11 12 13 14 10 11 |
|
*> 22 23 24 20 21 22 |
|
*> 33 34 30 31 32 33 |
|
*> 44 40 41 42 43 44 |
|
*> |
|
*> |
|
*> Let TRANSR = 'N'. RFP holds AP as follows: |
|
*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last |
|
*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of |
|
*> the transpose of the first two columns of AP upper. |
|
*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first |
|
*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of |
|
*> the transpose of the last two columns of AP lower. |
|
*> This covers the case N odd and TRANSR = 'N'. |
|
*> |
|
*> RFP A RFP A |
|
*> |
|
*> 02 03 04 00 33 43 |
|
*> 12 13 14 10 11 44 |
|
*> 22 23 24 20 21 22 |
|
*> 00 33 34 30 31 32 |
|
*> 01 11 44 40 41 42 |
|
*> |
|
*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the |
|
*> transpose of RFP A above. One therefore gets: |
|
*> |
|
*> RFP A RFP A |
|
*> |
|
*> 02 12 22 00 01 00 10 20 30 40 50 |
|
*> 03 13 23 33 11 33 11 21 31 41 51 |
|
*> 04 14 24 34 44 43 44 22 32 42 52 |
|
*> \endverbatim |
|
* |
|
* ===================================================================== |
|
SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, |
|
$ B, LDB ) |
|
* |
|
* -- LAPACK computational routine (version 3.7.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
|
* December 2016 |
* |
* |
* .. |
|
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO |
CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO |
INTEGER LDB, M, N |
INTEGER LDB, M, N |
Line 19
|
Line 291
|
DOUBLE PRECISION A( 0: * ), B( 0: LDB-1, 0: * ) |
DOUBLE PRECISION A( 0: * ), B( 0: LDB-1, 0: * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* Level 3 BLAS like routine for A in RFP Format. |
|
* |
|
* DTFSM solves the matrix equation |
|
* |
|
* op( A )*X = alpha*B or X*op( A ) = alpha*B |
|
* |
|
* where alpha is a scalar, X and B are m by n matrices, A is a unit, or |
|
* non-unit, upper or lower triangular matrix and op( A ) is one of |
|
* |
|
* op( A ) = A or op( A ) = A**T. |
|
* |
|
* A is in Rectangular Full Packed (RFP) Format. |
|
* |
|
* The matrix X is overwritten on B. |
|
* |
|
* Arguments |
|
* ========== |
|
* |
|
* TRANSR (input) CHARACTER*1 |
|
* = 'N': The Normal Form of RFP A is stored; |
|
* = 'T': The Transpose Form of RFP A is stored. |
|
* |
|
* SIDE (input) CHARACTER*1 |
|
* On entry, SIDE specifies whether op( A ) appears on the left |
|
* or right of X as follows: |
|
* |
|
* SIDE = 'L' or 'l' op( A )*X = alpha*B. |
|
* |
|
* SIDE = 'R' or 'r' X*op( A ) = alpha*B. |
|
* |
|
* Unchanged on exit. |
|
* |
|
* UPLO (input) CHARACTER*1 |
|
* On entry, UPLO specifies whether the RFP matrix A came from |
|
* an upper or lower triangular matrix as follows: |
|
* UPLO = 'U' or 'u' RFP A came from an upper triangular matrix |
|
* UPLO = 'L' or 'l' RFP A came from a lower triangular matrix |
|
* |
|
* Unchanged on exit. |
|
* |
|
* TRANS (input) CHARACTER*1 |
|
* On entry, TRANS specifies the form of op( A ) to be used |
|
* in the matrix multiplication as follows: |
|
* |
|
* TRANS = 'N' or 'n' op( A ) = A. |
|
* |
|
* TRANS = 'T' or 't' op( A ) = A'. |
|
* |
|
* Unchanged on exit. |
|
* |
|
* DIAG (input) CHARACTER*1 |
|
* On entry, DIAG specifies whether or not RFP A is unit |
|
* triangular as follows: |
|
* |
|
* DIAG = 'U' or 'u' A is assumed to be unit triangular. |
|
* |
|
* DIAG = 'N' or 'n' A is not assumed to be unit |
|
* triangular. |
|
* |
|
* Unchanged on exit. |
|
* |
|
* M (input) INTEGER |
|
* On entry, M specifies the number of rows of B. M must be at |
|
* least zero. |
|
* Unchanged on exit. |
|
* |
|
* N (input) INTEGER |
|
* On entry, N specifies the number of columns of B. N must be |
|
* at least zero. |
|
* Unchanged on exit. |
|
* |
|
* ALPHA (input) DOUBLE PRECISION |
|
* On entry, ALPHA specifies the scalar alpha. When alpha is |
|
* zero then A is not referenced and B need not be set before |
|
* entry. |
|
* Unchanged on exit. |
|
* |
|
* A (input) DOUBLE PRECISION array, dimension (NT) |
|
* NT = N*(N+1)/2. On entry, the matrix A in RFP Format. |
|
* RFP Format is described by TRANSR, UPLO and N as follows: |
|
* If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; |
|
* K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If |
|
* TRANSR = 'T' then RFP is the transpose of RFP A as |
|
* defined when TRANSR = 'N'. The contents of RFP A are defined |
|
* by UPLO as follows: If UPLO = 'U' the RFP A contains the NT |
|
* elements of upper packed A either in normal or |
|
* transpose Format. If UPLO = 'L' the RFP A contains |
|
* the NT elements of lower packed A either in normal or |
|
* transpose Format. The LDA of RFP A is (N+1)/2 when |
|
* TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is |
|
* even and is N when is odd. |
|
* See the Note below for more details. Unchanged on exit. |
|
* |
|
* B (input/output) DOUBLE PRECISION array, dimension (LDB,N) |
|
* Before entry, the leading m by n part of the array B must |
|
* contain the right-hand side matrix B, and on exit is |
|
* overwritten by the solution matrix X. |
|
* |
|
* LDB (input) INTEGER |
|
* On entry, LDB specifies the first dimension of B as declared |
|
* in the calling (sub) program. LDB must be at least |
|
* max( 1, m ). |
|
* Unchanged on exit. |
|
* |
|
* Further Details |
|
* =============== |
|
* |
|
* We first consider Rectangular Full Packed (RFP) Format when N is |
|
* even. We give an example where N = 6. |
|
* |
|
* AP is Upper AP is Lower |
|
* |
|
* 00 01 02 03 04 05 00 |
|
* 11 12 13 14 15 10 11 |
|
* 22 23 24 25 20 21 22 |
|
* 33 34 35 30 31 32 33 |
|
* 44 45 40 41 42 43 44 |
|
* 55 50 51 52 53 54 55 |
|
* |
|
* |
|
* Let TRANSR = 'N'. RFP holds AP as follows: |
|
* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last |
|
* three columns of AP upper. The lower triangle A(4:6,0:2) consists of |
|
* the transpose of the first three columns of AP upper. |
|
* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first |
|
* three columns of AP lower. The upper triangle A(0:2,0:2) consists of |
|
* the transpose of the last three columns of AP lower. |
|
* This covers the case N even and TRANSR = 'N'. |
|
* |
|
* RFP A RFP A |
|
* |
|
* 03 04 05 33 43 53 |
|
* 13 14 15 00 44 54 |
|
* 23 24 25 10 11 55 |
|
* 33 34 35 20 21 22 |
|
* 00 44 45 30 31 32 |
|
* 01 11 55 40 41 42 |
|
* 02 12 22 50 51 52 |
|
* |
|
* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the |
|
* transpose of RFP A above. One therefore gets: |
|
* |
|
* |
|
* RFP A RFP A |
|
* |
|
* 03 13 23 33 00 01 02 33 00 10 20 30 40 50 |
|
* 04 14 24 34 44 11 12 43 44 11 21 31 41 51 |
|
* 05 15 25 35 45 55 22 53 54 55 22 32 42 52 |
|
* |
|
* |
|
* We then consider Rectangular Full Packed (RFP) Format when N is |
|
* odd. We give an example where N = 5. |
|
* |
|
* AP is Upper AP is Lower |
|
* |
|
* 00 01 02 03 04 00 |
|
* 11 12 13 14 10 11 |
|
* 22 23 24 20 21 22 |
|
* 33 34 30 31 32 33 |
|
* 44 40 41 42 43 44 |
|
* |
|
* |
|
* Let TRANSR = 'N'. RFP holds AP as follows: |
|
* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last |
|
* three columns of AP upper. The lower triangle A(3:4,0:1) consists of |
|
* the transpose of the first two columns of AP upper. |
|
* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first |
|
* three columns of AP lower. The upper triangle A(0:1,1:2) consists of |
|
* the transpose of the last two columns of AP lower. |
|
* This covers the case N odd and TRANSR = 'N'. |
|
* |
|
* RFP A RFP A |
|
* |
|
* 02 03 04 00 33 43 |
|
* 12 13 14 10 11 44 |
|
* 22 23 24 20 21 22 |
|
* 00 33 34 30 31 32 |
|
* 01 11 44 40 41 42 |
|
* |
|
* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the |
|
* transpose of RFP A above. One therefore gets: |
|
* |
|
* RFP A RFP A |
|
* |
|
* 02 12 22 00 01 00 10 20 30 40 50 |
|
* 03 13 23 33 11 33 11 21 31 41 51 |
|
* 04 14 24 34 44 43 44 22 32 42 52 |
|
* |
|
* Reference |
|
* ========= |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. |
* .. |