--- rpl/lapack/lapack/dsytrs2.f 2010/12/21 13:53:40 1.2
+++ rpl/lapack/lapack/dsytrs2.f 2023/08/07 08:39:11 1.15
@@ -1,12 +1,138 @@
- SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+*> \brief \b DSYTRS2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSYTRS2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+* WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, LDB, N, NRHS
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DSYTRS2 solves a system of linear equations A*X = B with a real
+*> symmetric matrix A using the factorization A = U*D*U**T or
+*> A = L*D*L**T computed by DSYTRF and converted by DSYCONV.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the details of the factorization are stored
+*> as an upper or lower triangular matrix.
+*> = 'U': Upper triangular, form is A = U*D*U**T;
+*> = 'L': Lower triangular, form is A = L*D*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> The block diagonal matrix D and the multipliers used to
+*> obtain the factor U or L as computed by DSYTRF.
+*> Note that A is input / output. This might be counter-intuitive,
+*> and one may think that A is input only. A is input / output. This
+*> is because, at the start of the subroutine, we permute A in a
+*> "better" form and then we permute A back to its original form at
+*> the end.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges and the block structure of D
+*> as determined by DSYTRF.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
+*> On entry, the right hand side matrix B.
+*> On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleSYcomputational
+*
+* =====================================================================
+ SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
$ WORK, INFO )
*
-* -- LAPACK PROTOTYPE routine (version 3.3.0) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2010
-*
-* -- Written by Julie Langou of the Univ. of TN --
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -17,53 +143,6 @@
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DSYTRS2 solves a system of linear equations A*X = B with a real
-* symmetric matrix A using the factorization A = U*D*U**T or
-* A = L*D*L**T computed by DSYTRF and converted by DSYCONV.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the details of the factorization are stored
-* as an upper or lower triangular matrix.
-* = 'U': Upper triangular, form is A = U*D*U**T;
-* = 'L': Lower triangular, form is A = L*D*L**T.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* NRHS (input) INTEGER
-* The number of right hand sides, i.e., the number of columns
-* of the matrix B. NRHS >= 0.
-*
-* A (input) DOUBLE PRECISION array, dimension (LDA,N)
-* The block diagonal matrix D and the multipliers used to
-* obtain the factor U or L as computed by DSYTRF.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* IPIV (input) INTEGER array, dimension (N)
-* Details of the interchanges and the block structure of D
-* as determined by DSYTRF.
-*
-* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
-* On entry, the right hand side matrix B.
-* On exit, the solution matrix X.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,N).
-*
-* WORK (workspace) REAL array, dimension (N)
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-*
* =====================================================================
*
* .. Parameters ..
@@ -116,9 +195,9 @@
*
IF( UPPER ) THEN
*
-* Solve A*X = B, where A = U*D*U'.
+* Solve A*X = B, where A = U*D*U**T.
*
-* P' * B
+* P**T * B
K=N
DO WHILE ( K .GE. 1 )
IF( IPIV( K ).GT.0 ) THEN
@@ -138,16 +217,16 @@
END IF
END DO
*
-* Compute (U \P' * B) -> B [ (U \P' * B) ]
+* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
+*
+ CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
*
- CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,N,B,N)
+* Compute D \ B -> B [ D \ (U \P**T * B) ]
*
-* Compute D \ B -> B [ D \ (U \P' * B) ]
-*
I=N
DO WHILE ( I .GE. 1 )
IF( IPIV(I) .GT. 0 ) THEN
- CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N )
+ CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
ELSEIF ( I .GT. 1) THEN
IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN
AKM1K = WORK(I)
@@ -166,11 +245,11 @@
I = I - 1
END DO
*
-* Compute (U' \ B) -> B [ U' \ (D \ (U \P' * B) ) ]
+* Compute (U**T \ B) -> B [ U**T \ (D \ (U \P**T * B) ) ]
*
- CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,N,B,N)
+ CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB)
*
-* P * B [ P * (U' \ (D \ (U \P' * B) )) ]
+* P * B [ P * (U**T \ (D \ (U \P**T * B) )) ]
*
K=1
DO WHILE ( K .LE. N )
@@ -193,9 +272,9 @@
*
ELSE
*
-* Solve A*X = B, where A = L*D*L'.
+* Solve A*X = B, where A = L*D*L**T.
*
-* P' * B
+* P**T * B
K=1
DO WHILE ( K .LE. N )
IF( IPIV( K ).GT.0 ) THEN
@@ -215,16 +294,16 @@
ENDIF
END DO
*
-* Compute (L \P' * B) -> B [ (L \P' * B) ]
+* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
*
- CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,N,B,N)
+ CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
+*
+* Compute D \ B -> B [ D \ (L \P**T * B) ]
*
-* Compute D \ B -> B [ D \ (L \P' * B) ]
-*
I=1
DO WHILE ( I .LE. N )
IF( IPIV(I) .GT. 0 ) THEN
- CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N )
+ CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
ELSE
AKM1K = WORK(I)
AKM1 = A( I, I ) / AKM1K
@@ -241,11 +320,11 @@
I = I + 1
END DO
*
-* Compute (L' \ B) -> B [ L' \ (D \ (L \P' * B) ) ]
-*
- CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,N,B,N)
+* Compute (L**T \ B) -> B [ L**T \ (D \ (L \P**T * B) ) ]
+*
+ CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB)
*
-* P * B [ P * (L' \ (D \ (L \P' * B) )) ]
+* P * B [ P * (L**T \ (D \ (L \P**T * B) )) ]
*
K=N
DO WHILE ( K .GE. 1 )