--- rpl/lapack/lapack/dtfsm.f 2011/07/22 07:38:12 1.6
+++ rpl/lapack/lapack/dtfsm.f 2011/11/21 20:43:05 1.7
@@ -1,15 +1,287 @@
- SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
- $ B, LDB )
+*> \brief \b DTFSM
+*
+* =========== 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 --
-* -- April 2011 --
+*> \htmlonly
+*> Download DTFSM + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \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 November 2011
+*
+*> \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 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
*
-* ..
* .. Scalar Arguments ..
CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO
INTEGER LDB, M, N
@@ -19,200 +291,6 @@
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
-* =========
-*
* =====================================================================
*
* ..