Add graph references
This commit is contained in:
Abdelrahman Said
+539
@@ -0,0 +1,539 @@
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/* -- translated by f2c (version 20240504).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* > \brief \b DTRSM
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=========== DOCUMENTATION ===========
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Online html documentation available at
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http://www.netlib.org/lapack/explore-html/
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Definition:
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===========
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SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
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DOUBLE PRECISION ALPHA
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INTEGER LDA,LDB,M,N
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CHARACTER DIAG,SIDE,TRANSA,UPLO
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DOUBLE PRECISION A(LDA,*),B(LDB,*)
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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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> DTRSM solves one of the matrix equations
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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**T.
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>
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> The matrix X is overwritten on B.
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> \endverbatim
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Arguments:
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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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> \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 matrix A is an upper or
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> lower triangular matrix as follows:
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>
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> UPLO = 'U' or 'u' A is an upper triangular matrix.
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>
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> UPLO = 'L' or 'l' A is a lower triangular matrix.
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> \endverbatim
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>
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> \param[in] TRANSA
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> \verbatim
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> TRANSA is CHARACTER*1
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> On entry, TRANSA specifies the form of op( A ) to be used in
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> the matrix multiplication as follows:
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>
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> TRANSA = 'N' or 'n' op( A ) = A.
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>
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> TRANSA = 'T' or 't' op( A ) = A**T.
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>
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> TRANSA = 'C' or 'c' op( A ) = A**T.
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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 A is unit triangular
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> 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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> \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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> \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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> \endverbatim
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>
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> \param[in] ALPHA
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> \verbatim
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> ALPHA is DOUBLE PRECISION.
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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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> \endverbatim
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>
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> \param[in] A
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> \verbatim
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> A is DOUBLE PRECISION array, dimension ( LDA, k ),
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> where k is m when SIDE = 'L' or 'l'
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> and k is n when SIDE = 'R' or 'r'.
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> Before entry with UPLO = 'U' or 'u', the leading k by k
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> upper triangular part of the array A must contain the upper
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> triangular matrix and the strictly lower triangular part of
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> A is not referenced.
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> Before entry with UPLO = 'L' or 'l', the leading k by k
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> lower triangular part of the array A must contain the lower
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> triangular matrix and the strictly upper triangular part of
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> A is not referenced.
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> Note that when DIAG = 'U' or 'u', the diagonal elements of
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> A are not referenced either, but are assumed to be unity.
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> \endverbatim
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>
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> \param[in] LDA
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> \verbatim
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> LDA is INTEGER
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> On entry, LDA specifies the first dimension of A as declared
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> in the calling (sub) program. When SIDE = 'L' or 'l' then
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> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
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> then LDA must be at least max( 1, n ).
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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 DOUBLE PRECISION 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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> \endverbatim
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Authors:
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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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> \ingroup trsm
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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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> Level 3 Blas routine.
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>
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>
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> -- Written on 8-February-1989.
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> Jack Dongarra, Argonne National Laboratory.
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> Iain Duff, AERE Harwell.
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> Jeremy Du Croz, Numerical Algorithms Group Ltd.
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> Sven Hammarling, Numerical Algorithms Group Ltd.
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> \endverbatim
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>
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=====================================================================
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Subroutine */ int igraphdtrsm_(char *side, char *uplo, char *transa, char *diag,
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integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
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lda, doublereal *b, integer *ldb)
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{
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/* System generated locals */
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integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
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/* Local variables */
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integer i__, j, k, info;
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doublereal temp;
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logical lside;
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extern logical igraphlsame_(char *, char *);
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integer nrowa;
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logical upper;
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extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
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logical nounit;
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/* -- Reference BLAS level3 routine --
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-- Reference BLAS 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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=====================================================================
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Test the input parameters.
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Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1;
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b -= b_offset;
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/* Function Body */
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lside = igraphlsame_(side, "L");
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if (lside) {
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nrowa = *m;
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} else {
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nrowa = *n;
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}
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nounit = igraphlsame_(diag, "N");
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upper = igraphlsame_(uplo, "U");
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info = 0;
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if (! lside && ! igraphlsame_(side, "R")) {
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info = 1;
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} else if (! upper && ! igraphlsame_(uplo, "L")) {
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info = 2;
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} else if (! igraphlsame_(transa, "N") && ! igraphlsame_(transa,
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"T") && ! igraphlsame_(transa, "C")) {
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info = 3;
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} else if (! igraphlsame_(diag, "U") && ! igraphlsame_(diag,
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"N")) {
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info = 4;
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} else if (*m < 0) {
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info = 5;
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} else if (*n < 0) {
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info = 6;
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} else if (*lda < max(1,nrowa)) {
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info = 9;
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} else if (*ldb < max(1,*m)) {
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info = 11;
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}
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if (info != 0) {
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igraphxerbla_("DTRSM ", &info, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible. */
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if (*m == 0 || *n == 0) {
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return 0;
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}
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/* And when alpha.eq.zero. */
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if (*alpha == 0.) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] = 0.;
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/* L10: */
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}
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/* L20: */
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}
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return 0;
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}
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/* Start the operations. */
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if (lside) {
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if (igraphlsame_(transa, "N")) {
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/* Form B := alpha*inv( A )*B. */
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if (upper) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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if (*alpha != 1.) {
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
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;
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/* L30: */
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}
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}
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for (k = *m; k >= 1; --k) {
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if (b[k + j * b_dim1] != 0.) {
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if (nounit) {
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b[k + j * b_dim1] /= a[k + k * a_dim1];
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}
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i__2 = k - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
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i__ + k * a_dim1];
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/* L40: */
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}
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}
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/* L50: */
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}
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/* L60: */
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
|
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if (*alpha != 1.) {
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
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;
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/* L70: */
|
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}
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}
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i__2 = *m;
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for (k = 1; k <= i__2; ++k) {
|
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if (b[k + j * b_dim1] != 0.) {
|
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if (nounit) {
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b[k + j * b_dim1] /= a[k + k * a_dim1];
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}
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i__3 = *m;
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for (i__ = k + 1; i__ <= i__3; ++i__) {
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b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
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i__ + k * a_dim1];
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/* L80: */
|
||||
}
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||||
}
|
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/* L90: */
|
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}
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||||
/* L100: */
|
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}
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||||
}
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} else {
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||||
|
||||
/* Form B := alpha*inv( A**T )*B. */
|
||||
|
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if (upper) {
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i__1 = *n;
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||||
for (j = 1; j <= i__1; ++j) {
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
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temp = *alpha * b[i__ + j * b_dim1];
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||||
i__3 = i__ - 1;
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for (k = 1; k <= i__3; ++k) {
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temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
|
||||
/* L110: */
|
||||
}
|
||||
if (nounit) {
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||||
temp /= a[i__ + i__ * a_dim1];
|
||||
}
|
||||
b[i__ + j * b_dim1] = temp;
|
||||
/* L120: */
|
||||
}
|
||||
/* L130: */
|
||||
}
|
||||
} else {
|
||||
i__1 = *n;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
for (i__ = *m; i__ >= 1; --i__) {
|
||||
temp = *alpha * b[i__ + j * b_dim1];
|
||||
i__2 = *m;
|
||||
for (k = i__ + 1; k <= i__2; ++k) {
|
||||
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
|
||||
/* L140: */
|
||||
}
|
||||
if (nounit) {
|
||||
temp /= a[i__ + i__ * a_dim1];
|
||||
}
|
||||
b[i__ + j * b_dim1] = temp;
|
||||
/* L150: */
|
||||
}
|
||||
/* L160: */
|
||||
}
|
||||
}
|
||||
}
|
||||
} else {
|
||||
if (igraphlsame_(transa, "N")) {
|
||||
|
||||
/* Form B := alpha*B*inv( A ). */
|
||||
|
||||
if (upper) {
|
||||
i__1 = *n;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
if (*alpha != 1.) {
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
|
||||
;
|
||||
/* L170: */
|
||||
}
|
||||
}
|
||||
i__2 = j - 1;
|
||||
for (k = 1; k <= i__2; ++k) {
|
||||
if (a[k + j * a_dim1] != 0.) {
|
||||
i__3 = *m;
|
||||
for (i__ = 1; i__ <= i__3; ++i__) {
|
||||
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
|
||||
i__ + k * b_dim1];
|
||||
/* L180: */
|
||||
}
|
||||
}
|
||||
/* L190: */
|
||||
}
|
||||
if (nounit) {
|
||||
temp = 1. / a[j + j * a_dim1];
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
|
||||
/* L200: */
|
||||
}
|
||||
}
|
||||
/* L210: */
|
||||
}
|
||||
} else {
|
||||
for (j = *n; j >= 1; --j) {
|
||||
if (*alpha != 1.) {
|
||||
i__1 = *m;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
|
||||
;
|
||||
/* L220: */
|
||||
}
|
||||
}
|
||||
i__1 = *n;
|
||||
for (k = j + 1; k <= i__1; ++k) {
|
||||
if (a[k + j * a_dim1] != 0.) {
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
|
||||
i__ + k * b_dim1];
|
||||
/* L230: */
|
||||
}
|
||||
}
|
||||
/* L240: */
|
||||
}
|
||||
if (nounit) {
|
||||
temp = 1. / a[j + j * a_dim1];
|
||||
i__1 = *m;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
|
||||
/* L250: */
|
||||
}
|
||||
}
|
||||
/* L260: */
|
||||
}
|
||||
}
|
||||
} else {
|
||||
|
||||
/* Form B := alpha*B*inv( A**T ). */
|
||||
|
||||
if (upper) {
|
||||
for (k = *n; k >= 1; --k) {
|
||||
if (nounit) {
|
||||
temp = 1. / a[k + k * a_dim1];
|
||||
i__1 = *m;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
|
||||
/* L270: */
|
||||
}
|
||||
}
|
||||
i__1 = k - 1;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
if (a[j + k * a_dim1] != 0.) {
|
||||
temp = a[j + k * a_dim1];
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
b[i__ + j * b_dim1] -= temp * b[i__ + k *
|
||||
b_dim1];
|
||||
/* L280: */
|
||||
}
|
||||
}
|
||||
/* L290: */
|
||||
}
|
||||
if (*alpha != 1.) {
|
||||
i__1 = *m;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
|
||||
;
|
||||
/* L300: */
|
||||
}
|
||||
}
|
||||
/* L310: */
|
||||
}
|
||||
} else {
|
||||
i__1 = *n;
|
||||
for (k = 1; k <= i__1; ++k) {
|
||||
if (nounit) {
|
||||
temp = 1. / a[k + k * a_dim1];
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
|
||||
/* L320: */
|
||||
}
|
||||
}
|
||||
i__2 = *n;
|
||||
for (j = k + 1; j <= i__2; ++j) {
|
||||
if (a[j + k * a_dim1] != 0.) {
|
||||
temp = a[j + k * a_dim1];
|
||||
i__3 = *m;
|
||||
for (i__ = 1; i__ <= i__3; ++i__) {
|
||||
b[i__ + j * b_dim1] -= temp * b[i__ + k *
|
||||
b_dim1];
|
||||
/* L330: */
|
||||
}
|
||||
}
|
||||
/* L340: */
|
||||
}
|
||||
if (*alpha != 1.) {
|
||||
i__2 = *m;
|
||||
for (i__ = 1; i__ <= i__2; ++i__) {
|
||||
b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
|
||||
;
|
||||
/* L350: */
|
||||
}
|
||||
}
|
||||
/* L360: */
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return 0;
|
||||
|
||||
/* End of DTRSM */
|
||||
|
||||
} /* igraphdtrsm_ */
|
||||
|
||||
Reference in New Issue
Block a user