--- rpl/lapack/lapack/zhetrs2.f 2010/12/21 13:50:37 1.1
+++ rpl/lapack/lapack/zhetrs2.f 2017/06/17 11:06:49 1.12
@@ -1,13 +1,136 @@
- SUBROUTINE ZHETRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
- $ WORK, INFO )
+*> \brief \b ZHETRS2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
-* -- LAPACK PROTOTYPE routine (version 3.3.0) --
+*> \htmlonly
+*> Download ZHETRS2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHETRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+* WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, LDB, N, NRHS
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHETRS2 solves a system of linear equations A*X = B with a complex
+*> Hermitian matrix A using the factorization A = U*D*U**H or
+*> A = L*D*L**H computed by ZHETRF and converted by ZSYCONV.
+*> \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**H;
+*> = 'L': Lower triangular, form is A = L*D*L**H.
+*> \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] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> The block diagonal matrix D and the multipliers used to
+*> obtain the factor U or L as computed by ZHETRF.
+*> \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 ZHETRF.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 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 COMPLEX*16 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.
*
-* -- Written by Julie Langou of the Univ. of TN --
-* November 2010
+*> \date June 2016
+*
+*> \ingroup complex16HEcomputational
+*
+* =====================================================================
+ SUBROUTINE ZHETRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+ $ WORK, INFO )
*
+* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* June 2016
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -15,74 +138,27 @@
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
- DOUBLE COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
+ COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZHETRS2 solves a system of linear equations A*X = B with a real
-* Hermitian matrix A using the factorization A = U*D*U**T or
-* A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV.
-*
-* 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**H;
-* = 'L': Lower triangular, form is A = L*D*L**H.
-*
-* 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 COMPLEX array, dimension (LDA,N)
-* The block diagonal matrix D and the multipliers used to
-* obtain the factor U or L as computed by ZHETRF.
-*
-* 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 ZHETRF.
-*
-* B (input/output) DOUBLE COMPLEX 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 ..
- DOUBLE COMPLEX ONE
+ COMPLEX*16 ONE
PARAMETER ( ONE = (1.0D+0,0.0D+0) )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, IINFO, J, K, KP
DOUBLE PRECISION S
- DOUBLE COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM
+ COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
- EXTERNAL ZLACGV, ZSCAL, ZSYCONV, ZSWAP, ZTRSM, XERBLA
+ EXTERNAL ZDSCAL, ZSYCONV, ZSWAP, ZTRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCONJG, MAX
@@ -118,9 +194,9 @@
*
IF( UPPER ) THEN
*
-* Solve A*X = B, where A = U*D*U'.
+* Solve A*X = B, where A = U*D*U**H.
*
-* P' * B
+* P**T * B
K=N
DO WHILE ( K .GE. 1 )
IF( IPIV( K ).GT.0 ) THEN
@@ -140,12 +216,12 @@
END IF
END DO
*
-* Compute (U \P' * B) -> B [ (U \P' * B) ]
+* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
+*
+ CALL ZTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
*
- CALL ZTRSM('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
@@ -169,11 +245,11 @@
I = I - 1
END DO
*
-* Compute (U' \ B) -> B [ U' \ (D \ (U \P' * B) ) ]
+* Compute (U**H \ B) -> B [ U**H \ (D \ (U \P**T * B) ) ]
*
- CALL ZTRSM('L','U','C','U',N,NRHS,ONE,A,N,B,N)
+ CALL ZTRSM('L','U','C','U',N,NRHS,ONE,A,LDA,B,LDB)
*
-* P * B [ P * (U' \ (D \ (U \P' * B) )) ]
+* P * B [ P * (U**H \ (D \ (U \P**T * B) )) ]
*
K=1
DO WHILE ( K .LE. N )
@@ -196,9 +272,9 @@
*
ELSE
*
-* Solve A*X = B, where A = L*D*L'.
+* Solve A*X = B, where A = L*D*L**H.
*
-* P' * B
+* P**T * B
K=1
DO WHILE ( K .LE. N )
IF( IPIV( K ).GT.0 ) THEN
@@ -218,12 +294,12 @@
ENDIF
END DO
*
-* Compute (L \P' * B) -> B [ (L \P' * B) ]
+* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
*
- CALL ZTRSM('L','L','N','U',N,NRHS,ONE,A,N,B,N)
+ CALL ZTRSM('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
@@ -245,11 +321,11 @@
I = I + 1
END DO
*
-* Compute (L' \ B) -> B [ L' \ (D \ (L \P' * B) ) ]
-*
- CALL ZTRSM('L','L','C','U',N,NRHS,ONE,A,N,B,N)
+* Compute (L**H \ B) -> B [ L**H \ (D \ (L \P**T * B) ) ]
+*
+ CALL ZTRSM('L','L','C','U',N,NRHS,ONE,A,LDA,B,LDB)
*
-* P * B [ P * (L' \ (D \ (L \P' * B) )) ]
+* P * B [ P * (L**H \ (D \ (L \P**T * B) )) ]
*
K=N
DO WHILE ( K .GE. 1 )