1027 lines
35 KiB
Fortran
1027 lines
35 KiB
Fortran
*> \brief \b ZTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download ZTFSM + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztfsm.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztfsm.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztfsm.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
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* B, LDB )
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*
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* .. Scalar Arguments ..
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* CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO
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* INTEGER LDB, M, N
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* COMPLEX*16 ALPHA
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A( 0: * ), B( 0: LDB-1, 0: * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> Level 3 BLAS like routine for A in RFP Format.
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*>
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*> ZTFSM solves the matrix equation
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*>
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*> op( A )*X = alpha*B or X*op( A ) = alpha*B
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*>
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*> where alpha is a scalar, X and B are m by n matrices, A is a unit, or
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*> non-unit, upper or lower triangular matrix and op( A ) is one of
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*>
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*> op( A ) = A or op( A ) = A**H.
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*>
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*> A is in Rectangular Full Packed (RFP) Format.
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*>
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*> The matrix X is overwritten on B.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] TRANSR
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*> \verbatim
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*> TRANSR is CHARACTER*1
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*> = 'N': The Normal Form of RFP A is stored;
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*> = 'C': The Conjugate-transpose Form of RFP A is stored.
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*> \endverbatim
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*>
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*> \param[in] SIDE
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*> \verbatim
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*> SIDE is CHARACTER*1
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*> On entry, SIDE specifies whether op( A ) appears on the left
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*> or right of X as follows:
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*>
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*> SIDE = 'L' or 'l' op( A )*X = alpha*B.
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*>
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*> SIDE = 'R' or 'r' X*op( A ) = alpha*B.
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*>
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> On entry, UPLO specifies whether the RFP matrix A came from
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*> an upper or lower triangular matrix as follows:
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*> UPLO = 'U' or 'u' RFP A came from an upper triangular matrix
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*> UPLO = 'L' or 'l' RFP A came from a lower triangular matrix
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*>
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> On entry, TRANS specifies the form of op( A ) to be used
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*> in the matrix multiplication as follows:
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*>
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*> TRANS = 'N' or 'n' op( A ) = A.
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*>
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*> TRANS = 'C' or 'c' op( A ) = conjg( A' ).
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*>
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> On entry, DIAG specifies whether or not RFP A is unit
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*> triangular as follows:
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*>
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*> DIAG = 'U' or 'u' A is assumed to be unit triangular.
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*>
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*> DIAG = 'N' or 'n' A is not assumed to be unit
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*> triangular.
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*>
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> On entry, M specifies the number of rows of B. M must be at
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*> least zero.
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> On entry, N specifies the number of columns of B. N must be
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*> at least zero.
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] ALPHA
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*> \verbatim
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*> ALPHA is COMPLEX*16
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*> On entry, ALPHA specifies the scalar alpha. When alpha is
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*> zero then A is not referenced and B need not be set before
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*> entry.
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (N*(N+1)/2)
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*> NT = N*(N+1)/2. On entry, the matrix A in RFP Format.
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*> RFP Format is described by TRANSR, UPLO and N as follows:
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*> If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
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*> K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
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*> TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A as
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*> defined when TRANSR = 'N'. The contents of RFP A are defined
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*> by UPLO as follows: If UPLO = 'U' the RFP A contains the NT
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*> elements of upper packed A either in normal or
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*> conjugate-transpose Format. If UPLO = 'L' the RFP A contains
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*> the NT elements of lower packed A either in normal or
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*> conjugate-transpose Format. The LDA of RFP A is (N+1)/2 when
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*> TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
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*> even and is N when is odd.
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*> See the Note below for more details. Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension (LDB,N)
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*> Before entry, the leading m by n part of the array B must
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*> contain the right-hand side matrix B, and on exit is
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*> overwritten by the solution matrix X.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> On entry, LDB specifies the first dimension of B as declared
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*> in the calling (sub) program. LDB must be at least
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*> max( 1, m ).
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*> Unchanged on exit.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date September 2012
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*
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*> \ingroup complex16OTHERcomputational
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> We first consider Standard Packed Format when N is even.
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*> We give an example where N = 6.
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*>
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*> AP is Upper AP is Lower
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*>
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*> 00 01 02 03 04 05 00
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*> 11 12 13 14 15 10 11
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*> 22 23 24 25 20 21 22
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*> 33 34 35 30 31 32 33
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*> 44 45 40 41 42 43 44
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*> 55 50 51 52 53 54 55
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*>
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*>
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*> Let TRANSR = 'N'. RFP holds AP as follows:
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*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
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*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
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*> conjugate-transpose of the first three columns of AP upper.
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*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
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*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
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*> conjugate-transpose of the last three columns of AP lower.
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*> To denote conjugate we place -- above the element. This covers the
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*> case N even and TRANSR = 'N'.
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*>
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*> RFP A RFP A
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*>
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*> -- -- --
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*> 03 04 05 33 43 53
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*> -- --
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*> 13 14 15 00 44 54
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*> --
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*> 23 24 25 10 11 55
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*>
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*> 33 34 35 20 21 22
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*> --
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*> 00 44 45 30 31 32
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*> -- --
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*> 01 11 55 40 41 42
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*> -- -- --
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*> 02 12 22 50 51 52
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*>
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*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
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*> transpose of RFP A above. One therefore gets:
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*>
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*>
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*> RFP A RFP A
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*>
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*> -- -- -- -- -- -- -- -- -- --
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*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
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*> -- -- -- -- -- -- -- -- -- --
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*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
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*> -- -- -- -- -- -- -- -- -- --
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*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
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*>
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*>
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*> We next consider Standard Packed Format when N is odd.
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*> We give an example where N = 5.
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*>
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*> AP is Upper AP is Lower
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*>
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*> 00 01 02 03 04 00
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*> 11 12 13 14 10 11
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*> 22 23 24 20 21 22
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*> 33 34 30 31 32 33
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*> 44 40 41 42 43 44
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*>
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*>
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*> Let TRANSR = 'N'. RFP holds AP as follows:
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*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
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*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
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*> conjugate-transpose of the first two columns of AP upper.
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*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
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*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
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*> conjugate-transpose of the last two columns of AP lower.
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*> To denote conjugate we place -- above the element. This covers the
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*> case N odd and TRANSR = 'N'.
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*>
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*> RFP A RFP A
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*>
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*> -- --
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*> 02 03 04 00 33 43
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*> --
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*> 12 13 14 10 11 44
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*>
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*> 22 23 24 20 21 22
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*> --
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*> 00 33 34 30 31 32
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*> -- --
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*> 01 11 44 40 41 42
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*>
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*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
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*> transpose of RFP A above. One therefore gets:
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*>
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*>
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*> RFP A RFP A
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*>
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*> -- -- -- -- -- -- -- -- --
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*> 02 12 22 00 01 00 10 20 30 40 50
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*> -- -- -- -- -- -- -- -- --
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*> 03 13 23 33 11 33 11 21 31 41 51
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*> -- -- -- -- -- -- -- -- --
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*> 04 14 24 34 44 43 44 22 32 42 52
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
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$ B, LDB )
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*
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* -- LAPACK computational routine (version 3.4.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* September 2012
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*
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* .. Scalar Arguments ..
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CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO
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INTEGER LDB, M, N
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COMPLEX*16 ALPHA
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A( 0: * ), B( 0: LDB-1, 0: * )
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* ..
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*
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* =====================================================================
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* ..
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* .. Parameters ..
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COMPLEX*16 CONE, CZERO
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PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
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$ CZERO = ( 0.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL LOWER, LSIDE, MISODD, NISODD, NORMALTRANSR,
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$ NOTRANS
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INTEGER M1, M2, N1, N2, K, INFO, I, J
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZGEMM, ZTRSM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MOD
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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NORMALTRANSR = LSAME( TRANSR, 'N' )
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LSIDE = LSAME( SIDE, 'L' )
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LOWER = LSAME( UPLO, 'L' )
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NOTRANS = LSAME( TRANS, 'N' )
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IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.LSIDE .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
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INFO = -2
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ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
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INFO = -3
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ELSE IF( .NOT.NOTRANS .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
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INFO = -4
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ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
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$ THEN
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INFO = -5
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ELSE IF( M.LT.0 ) THEN
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INFO = -6
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ELSE IF( N.LT.0 ) THEN
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INFO = -7
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ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
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INFO = -11
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZTFSM ', -INFO )
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RETURN
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END IF
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*
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* Quick return when ( (N.EQ.0).OR.(M.EQ.0) )
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*
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IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
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$ RETURN
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*
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* Quick return when ALPHA.EQ.(0D+0,0D+0)
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*
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IF( ALPHA.EQ.CZERO ) THEN
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DO 20 J = 0, N - 1
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DO 10 I = 0, M - 1
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B( I, J ) = CZERO
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10 CONTINUE
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20 CONTINUE
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RETURN
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END IF
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*
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IF( LSIDE ) THEN
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*
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* SIDE = 'L'
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*
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* A is M-by-M.
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* If M is odd, set NISODD = .TRUE., and M1 and M2.
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* If M is even, NISODD = .FALSE., and M.
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*
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IF( MOD( M, 2 ).EQ.0 ) THEN
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MISODD = .FALSE.
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K = M / 2
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ELSE
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MISODD = .TRUE.
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IF( LOWER ) THEN
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M2 = M / 2
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M1 = M - M2
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ELSE
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M1 = M / 2
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M2 = M - M1
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END IF
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END IF
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*
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IF( MISODD ) THEN
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*
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* SIDE = 'L' and N is odd
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*
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IF( NORMALTRANSR ) THEN
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*
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* SIDE = 'L', N is odd, and TRANSR = 'N'
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*
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IF( LOWER ) THEN
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*
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* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'L'
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*
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IF( NOTRANS ) THEN
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*
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* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and
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* TRANS = 'N'
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*
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IF( M.EQ.1 ) THEN
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CALL ZTRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA,
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$ A, M, B, LDB )
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ELSE
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CALL ZTRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA,
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$ A( 0 ), M, B, LDB )
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CALL ZGEMM( 'N', 'N', M2, N, M1, -CONE, A( M1 ),
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$ M, B, LDB, ALPHA, B( M1, 0 ), LDB )
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CALL ZTRSM( 'L', 'U', 'C', DIAG, M2, N, CONE,
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$ A( M ), M, B( M1, 0 ), LDB )
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END IF
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*
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ELSE
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*
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* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and
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* TRANS = 'C'
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*
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IF( M.EQ.1 ) THEN
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CALL ZTRSM( 'L', 'L', 'C', DIAG, M1, N, ALPHA,
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$ A( 0 ), M, B, LDB )
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ELSE
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CALL ZTRSM( 'L', 'U', 'N', DIAG, M2, N, ALPHA,
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$ A( M ), M, B( M1, 0 ), LDB )
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CALL ZGEMM( 'C', 'N', M1, N, M2, -CONE, A( M1 ),
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$ M, B( M1, 0 ), LDB, ALPHA, B, LDB )
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CALL ZTRSM( 'L', 'L', 'C', DIAG, M1, N, CONE,
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$ A( 0 ), M, B, LDB )
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END IF
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*
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END IF
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*
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ELSE
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*
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* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'U'
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*
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IF( .NOT.NOTRANS ) THEN
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*
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* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and
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* TRANS = 'N'
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*
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CALL ZTRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA,
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$ A( M2 ), M, B, LDB )
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CALL ZGEMM( 'C', 'N', M2, N, M1, -CONE, A( 0 ), M,
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$ B, LDB, ALPHA, B( M1, 0 ), LDB )
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CALL ZTRSM( 'L', 'U', 'C', DIAG, M2, N, CONE,
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$ A( M1 ), M, B( M1, 0 ), LDB )
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*
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ELSE
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*
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* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and
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* TRANS = 'C'
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*
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CALL ZTRSM( 'L', 'U', 'N', DIAG, M2, N, ALPHA,
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$ A( M1 ), M, B( M1, 0 ), LDB )
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CALL ZGEMM( 'N', 'N', M1, N, M2, -CONE, A( 0 ), M,
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$ B( M1, 0 ), LDB, ALPHA, B, LDB )
|
|
CALL ZTRSM( 'L', 'L', 'C', DIAG, M1, N, CONE,
|
|
$ A( M2 ), M, B, LDB )
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE = 'L', N is odd, and TRANSR = 'C'
|
|
*
|
|
IF( LOWER ) THEN
|
|
*
|
|
* SIDE ='L', N is odd, TRANSR = 'C', and UPLO = 'L'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'L', and
|
|
* TRANS = 'N'
|
|
*
|
|
IF( M.EQ.1 ) THEN
|
|
CALL ZTRSM( 'L', 'U', 'C', DIAG, M1, N, ALPHA,
|
|
$ A( 0 ), M1, B, LDB )
|
|
ELSE
|
|
CALL ZTRSM( 'L', 'U', 'C', DIAG, M1, N, ALPHA,
|
|
$ A( 0 ), M1, B, LDB )
|
|
CALL ZGEMM( 'C', 'N', M2, N, M1, -CONE,
|
|
$ A( M1*M1 ), M1, B, LDB, ALPHA,
|
|
$ B( M1, 0 ), LDB )
|
|
CALL ZTRSM( 'L', 'L', 'N', DIAG, M2, N, CONE,
|
|
$ A( 1 ), M1, B( M1, 0 ), LDB )
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'L', and
|
|
* TRANS = 'C'
|
|
*
|
|
IF( M.EQ.1 ) THEN
|
|
CALL ZTRSM( 'L', 'U', 'N', DIAG, M1, N, ALPHA,
|
|
$ A( 0 ), M1, B, LDB )
|
|
ELSE
|
|
CALL ZTRSM( 'L', 'L', 'C', DIAG, M2, N, ALPHA,
|
|
$ A( 1 ), M1, B( M1, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'N', M1, N, M2, -CONE,
|
|
$ A( M1*M1 ), M1, B( M1, 0 ), LDB,
|
|
$ ALPHA, B, LDB )
|
|
CALL ZTRSM( 'L', 'U', 'N', DIAG, M1, N, CONE,
|
|
$ A( 0 ), M1, B, LDB )
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='L', N is odd, TRANSR = 'C', and UPLO = 'U'
|
|
*
|
|
IF( .NOT.NOTRANS ) THEN
|
|
*
|
|
* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'U', and
|
|
* TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'L', 'U', 'C', DIAG, M1, N, ALPHA,
|
|
$ A( M2*M2 ), M2, B, LDB )
|
|
CALL ZGEMM( 'N', 'N', M2, N, M1, -CONE, A( 0 ), M2,
|
|
$ B, LDB, ALPHA, B( M1, 0 ), LDB )
|
|
CALL ZTRSM( 'L', 'L', 'N', DIAG, M2, N, CONE,
|
|
$ A( M1*M2 ), M2, B( M1, 0 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'U', and
|
|
* TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'L', 'L', 'C', DIAG, M2, N, ALPHA,
|
|
$ A( M1*M2 ), M2, B( M1, 0 ), LDB )
|
|
CALL ZGEMM( 'C', 'N', M1, N, M2, -CONE, A( 0 ), M2,
|
|
$ B( M1, 0 ), LDB, ALPHA, B, LDB )
|
|
CALL ZTRSM( 'L', 'U', 'N', DIAG, M1, N, CONE,
|
|
$ A( M2*M2 ), M2, B, LDB )
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE = 'L' and N is even
|
|
*
|
|
IF( NORMALTRANSR ) THEN
|
|
*
|
|
* SIDE = 'L', N is even, and TRANSR = 'N'
|
|
*
|
|
IF( LOWER ) THEN
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'L'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L',
|
|
* and TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'L', 'L', 'N', DIAG, K, N, ALPHA,
|
|
$ A( 1 ), M+1, B, LDB )
|
|
CALL ZGEMM( 'N', 'N', K, N, K, -CONE, A( K+1 ),
|
|
$ M+1, B, LDB, ALPHA, B( K, 0 ), LDB )
|
|
CALL ZTRSM( 'L', 'U', 'C', DIAG, K, N, CONE,
|
|
$ A( 0 ), M+1, B( K, 0 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L',
|
|
* and TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'L', 'U', 'N', DIAG, K, N, ALPHA,
|
|
$ A( 0 ), M+1, B( K, 0 ), LDB )
|
|
CALL ZGEMM( 'C', 'N', K, N, K, -CONE, A( K+1 ),
|
|
$ M+1, B( K, 0 ), LDB, ALPHA, B, LDB )
|
|
CALL ZTRSM( 'L', 'L', 'C', DIAG, K, N, CONE,
|
|
$ A( 1 ), M+1, B, LDB )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'U'
|
|
*
|
|
IF( .NOT.NOTRANS ) THEN
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U',
|
|
* and TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'L', 'L', 'N', DIAG, K, N, ALPHA,
|
|
$ A( K+1 ), M+1, B, LDB )
|
|
CALL ZGEMM( 'C', 'N', K, N, K, -CONE, A( 0 ), M+1,
|
|
$ B, LDB, ALPHA, B( K, 0 ), LDB )
|
|
CALL ZTRSM( 'L', 'U', 'C', DIAG, K, N, CONE,
|
|
$ A( K ), M+1, B( K, 0 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U',
|
|
* and TRANS = 'C'
|
|
CALL ZTRSM( 'L', 'U', 'N', DIAG, K, N, ALPHA,
|
|
$ A( K ), M+1, B( K, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'N', K, N, K, -CONE, A( 0 ), M+1,
|
|
$ B( K, 0 ), LDB, ALPHA, B, LDB )
|
|
CALL ZTRSM( 'L', 'L', 'C', DIAG, K, N, CONE,
|
|
$ A( K+1 ), M+1, B, LDB )
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE = 'L', N is even, and TRANSR = 'C'
|
|
*
|
|
IF( LOWER ) THEN
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'C', and UPLO = 'L'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'L',
|
|
* and TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'L', 'U', 'C', DIAG, K, N, ALPHA,
|
|
$ A( K ), K, B, LDB )
|
|
CALL ZGEMM( 'C', 'N', K, N, K, -CONE,
|
|
$ A( K*( K+1 ) ), K, B, LDB, ALPHA,
|
|
$ B( K, 0 ), LDB )
|
|
CALL ZTRSM( 'L', 'L', 'N', DIAG, K, N, CONE,
|
|
$ A( 0 ), K, B( K, 0 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'L',
|
|
* and TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'L', 'L', 'C', DIAG, K, N, ALPHA,
|
|
$ A( 0 ), K, B( K, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'N', K, N, K, -CONE,
|
|
$ A( K*( K+1 ) ), K, B( K, 0 ), LDB,
|
|
$ ALPHA, B, LDB )
|
|
CALL ZTRSM( 'L', 'U', 'N', DIAG, K, N, CONE,
|
|
$ A( K ), K, B, LDB )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'C', and UPLO = 'U'
|
|
*
|
|
IF( .NOT.NOTRANS ) THEN
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'U',
|
|
* and TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'L', 'U', 'C', DIAG, K, N, ALPHA,
|
|
$ A( K*( K+1 ) ), K, B, LDB )
|
|
CALL ZGEMM( 'N', 'N', K, N, K, -CONE, A( 0 ), K, B,
|
|
$ LDB, ALPHA, B( K, 0 ), LDB )
|
|
CALL ZTRSM( 'L', 'L', 'N', DIAG, K, N, CONE,
|
|
$ A( K*K ), K, B( K, 0 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'U',
|
|
* and TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'L', 'L', 'C', DIAG, K, N, ALPHA,
|
|
$ A( K*K ), K, B( K, 0 ), LDB )
|
|
CALL ZGEMM( 'C', 'N', K, N, K, -CONE, A( 0 ), K,
|
|
$ B( K, 0 ), LDB, ALPHA, B, LDB )
|
|
CALL ZTRSM( 'L', 'U', 'N', DIAG, K, N, CONE,
|
|
$ A( K*( K+1 ) ), K, B, LDB )
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE = 'R'
|
|
*
|
|
* A is N-by-N.
|
|
* If N is odd, set NISODD = .TRUE., and N1 and N2.
|
|
* If N is even, NISODD = .FALSE., and K.
|
|
*
|
|
IF( MOD( N, 2 ).EQ.0 ) THEN
|
|
NISODD = .FALSE.
|
|
K = N / 2
|
|
ELSE
|
|
NISODD = .TRUE.
|
|
IF( LOWER ) THEN
|
|
N2 = N / 2
|
|
N1 = N - N2
|
|
ELSE
|
|
N1 = N / 2
|
|
N2 = N - N1
|
|
END IF
|
|
END IF
|
|
*
|
|
IF( NISODD ) THEN
|
|
*
|
|
* SIDE = 'R' and N is odd
|
|
*
|
|
IF( NORMALTRANSR ) THEN
|
|
*
|
|
* SIDE = 'R', N is odd, and TRANSR = 'N'
|
|
*
|
|
IF( LOWER ) THEN
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'L'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and
|
|
* TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'R', 'U', 'C', DIAG, M, N2, ALPHA,
|
|
$ A( N ), N, B( 0, N1 ), LDB )
|
|
CALL ZGEMM( 'N', 'N', M, N1, N2, -CONE, B( 0, N1 ),
|
|
$ LDB, A( N1 ), N, ALPHA, B( 0, 0 ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'L', 'N', DIAG, M, N1, CONE,
|
|
$ A( 0 ), N, B( 0, 0 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and
|
|
* TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'R', 'L', 'C', DIAG, M, N1, ALPHA,
|
|
$ A( 0 ), N, B( 0, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'C', M, N2, N1, -CONE, B( 0, 0 ),
|
|
$ LDB, A( N1 ), N, ALPHA, B( 0, N1 ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'U', 'N', DIAG, M, N2, CONE,
|
|
$ A( N ), N, B( 0, N1 ), LDB )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'U'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and
|
|
* TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'R', 'L', 'C', DIAG, M, N1, ALPHA,
|
|
$ A( N2 ), N, B( 0, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'N', M, N2, N1, -CONE, B( 0, 0 ),
|
|
$ LDB, A( 0 ), N, ALPHA, B( 0, N1 ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'U', 'N', DIAG, M, N2, CONE,
|
|
$ A( N1 ), N, B( 0, N1 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and
|
|
* TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'R', 'U', 'C', DIAG, M, N2, ALPHA,
|
|
$ A( N1 ), N, B( 0, N1 ), LDB )
|
|
CALL ZGEMM( 'N', 'C', M, N1, N2, -CONE, B( 0, N1 ),
|
|
$ LDB, A( 0 ), N, ALPHA, B( 0, 0 ), LDB )
|
|
CALL ZTRSM( 'R', 'L', 'N', DIAG, M, N1, CONE,
|
|
$ A( N2 ), N, B( 0, 0 ), LDB )
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE = 'R', N is odd, and TRANSR = 'C'
|
|
*
|
|
IF( LOWER ) THEN
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'C', and UPLO = 'L'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'L', and
|
|
* TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'R', 'L', 'N', DIAG, M, N2, ALPHA,
|
|
$ A( 1 ), N1, B( 0, N1 ), LDB )
|
|
CALL ZGEMM( 'N', 'C', M, N1, N2, -CONE, B( 0, N1 ),
|
|
$ LDB, A( N1*N1 ), N1, ALPHA, B( 0, 0 ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'U', 'C', DIAG, M, N1, CONE,
|
|
$ A( 0 ), N1, B( 0, 0 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'L', and
|
|
* TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'R', 'U', 'N', DIAG, M, N1, ALPHA,
|
|
$ A( 0 ), N1, B( 0, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'N', M, N2, N1, -CONE, B( 0, 0 ),
|
|
$ LDB, A( N1*N1 ), N1, ALPHA, B( 0, N1 ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'L', 'C', DIAG, M, N2, CONE,
|
|
$ A( 1 ), N1, B( 0, N1 ), LDB )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'C', and UPLO = 'U'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'U', and
|
|
* TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'R', 'U', 'N', DIAG, M, N1, ALPHA,
|
|
$ A( N2*N2 ), N2, B( 0, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'C', M, N2, N1, -CONE, B( 0, 0 ),
|
|
$ LDB, A( 0 ), N2, ALPHA, B( 0, N1 ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'L', 'C', DIAG, M, N2, CONE,
|
|
$ A( N1*N2 ), N2, B( 0, N1 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'U', and
|
|
* TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'R', 'L', 'N', DIAG, M, N2, ALPHA,
|
|
$ A( N1*N2 ), N2, B( 0, N1 ), LDB )
|
|
CALL ZGEMM( 'N', 'N', M, N1, N2, -CONE, B( 0, N1 ),
|
|
$ LDB, A( 0 ), N2, ALPHA, B( 0, 0 ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'U', 'C', DIAG, M, N1, CONE,
|
|
$ A( N2*N2 ), N2, B( 0, 0 ), LDB )
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE = 'R' and N is even
|
|
*
|
|
IF( NORMALTRANSR ) THEN
|
|
*
|
|
* SIDE = 'R', N is even, and TRANSR = 'N'
|
|
*
|
|
IF( LOWER ) THEN
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'L'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L',
|
|
* and TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'R', 'U', 'C', DIAG, M, K, ALPHA,
|
|
$ A( 0 ), N+1, B( 0, K ), LDB )
|
|
CALL ZGEMM( 'N', 'N', M, K, K, -CONE, B( 0, K ),
|
|
$ LDB, A( K+1 ), N+1, ALPHA, B( 0, 0 ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'L', 'N', DIAG, M, K, CONE,
|
|
$ A( 1 ), N+1, B( 0, 0 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L',
|
|
* and TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'R', 'L', 'C', DIAG, M, K, ALPHA,
|
|
$ A( 1 ), N+1, B( 0, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'C', M, K, K, -CONE, B( 0, 0 ),
|
|
$ LDB, A( K+1 ), N+1, ALPHA, B( 0, K ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'U', 'N', DIAG, M, K, CONE,
|
|
$ A( 0 ), N+1, B( 0, K ), LDB )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'U'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U',
|
|
* and TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'R', 'L', 'C', DIAG, M, K, ALPHA,
|
|
$ A( K+1 ), N+1, B( 0, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'N', M, K, K, -CONE, B( 0, 0 ),
|
|
$ LDB, A( 0 ), N+1, ALPHA, B( 0, K ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'U', 'N', DIAG, M, K, CONE,
|
|
$ A( K ), N+1, B( 0, K ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U',
|
|
* and TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'R', 'U', 'C', DIAG, M, K, ALPHA,
|
|
$ A( K ), N+1, B( 0, K ), LDB )
|
|
CALL ZGEMM( 'N', 'C', M, K, K, -CONE, B( 0, K ),
|
|
$ LDB, A( 0 ), N+1, ALPHA, B( 0, 0 ),
|
|
$ LDB )
|
|
CALL ZTRSM( 'R', 'L', 'N', DIAG, M, K, CONE,
|
|
$ A( K+1 ), N+1, B( 0, 0 ), LDB )
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE = 'R', N is even, and TRANSR = 'C'
|
|
*
|
|
IF( LOWER ) THEN
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'C', and UPLO = 'L'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'L',
|
|
* and TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'R', 'L', 'N', DIAG, M, K, ALPHA,
|
|
$ A( 0 ), K, B( 0, K ), LDB )
|
|
CALL ZGEMM( 'N', 'C', M, K, K, -CONE, B( 0, K ),
|
|
$ LDB, A( ( K+1 )*K ), K, ALPHA,
|
|
$ B( 0, 0 ), LDB )
|
|
CALL ZTRSM( 'R', 'U', 'C', DIAG, M, K, CONE,
|
|
$ A( K ), K, B( 0, 0 ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'L',
|
|
* and TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'R', 'U', 'N', DIAG, M, K, ALPHA,
|
|
$ A( K ), K, B( 0, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'N', M, K, K, -CONE, B( 0, 0 ),
|
|
$ LDB, A( ( K+1 )*K ), K, ALPHA,
|
|
$ B( 0, K ), LDB )
|
|
CALL ZTRSM( 'R', 'L', 'C', DIAG, M, K, CONE,
|
|
$ A( 0 ), K, B( 0, K ), LDB )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'C', and UPLO = 'U'
|
|
*
|
|
IF( NOTRANS ) THEN
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'U',
|
|
* and TRANS = 'N'
|
|
*
|
|
CALL ZTRSM( 'R', 'U', 'N', DIAG, M, K, ALPHA,
|
|
$ A( ( K+1 )*K ), K, B( 0, 0 ), LDB )
|
|
CALL ZGEMM( 'N', 'C', M, K, K, -CONE, B( 0, 0 ),
|
|
$ LDB, A( 0 ), K, ALPHA, B( 0, K ), LDB )
|
|
CALL ZTRSM( 'R', 'L', 'C', DIAG, M, K, CONE,
|
|
$ A( K*K ), K, B( 0, K ), LDB )
|
|
*
|
|
ELSE
|
|
*
|
|
* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'U',
|
|
* and TRANS = 'C'
|
|
*
|
|
CALL ZTRSM( 'R', 'L', 'N', DIAG, M, K, ALPHA,
|
|
$ A( K*K ), K, B( 0, K ), LDB )
|
|
CALL ZGEMM( 'N', 'N', M, K, K, -CONE, B( 0, K ),
|
|
$ LDB, A( 0 ), K, ALPHA, B( 0, 0 ), LDB )
|
|
CALL ZTRSM( 'R', 'U', 'C', DIAG, M, K, CONE,
|
|
$ A( ( K+1 )*K ), K, B( 0, 0 ), LDB )
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of ZTFSM
|
|
*
|
|
END
|