coco
655 lines
25 KiB
C++
655 lines
25 KiB
C++
// Copyright (C) 2010 Davis E. King (davis@dlib.net)
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// License: Boost Software License See LICENSE.txt for the full license.
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#ifndef DLIB_MATRiX_TRSM_Hh_
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#define DLIB_MATRiX_TRSM_Hh_
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#include "lapack/fortran_id.h"
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#include "cblas_constants.h"
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namespace dlib
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{
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namespace blas_bindings
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{
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#ifdef DLIB_USE_BLAS
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#ifdef DLIB_DEFINE_CBLAS_API
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extern "C"
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{
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void cblas_strsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
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const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
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const CBLAS_DIAG Diag, const CBLAS_INT_TYPE M, const CBLAS_INT_TYPE N,
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const float alpha, const float *A, const CBLAS_INT_TYPE lda,
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float *B, const CBLAS_INT_TYPE ldb);
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void cblas_dtrsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
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const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
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const CBLAS_DIAG Diag, const CBLAS_INT_TYPE M, const CBLAS_INT_TYPE N,
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const double alpha, const double *A, const CBLAS_INT_TYPE lda,
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double *B, const CBLAS_INT_TYPE ldb);
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}
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#endif // if DLIB_DEFINE_CBLAS_API
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#endif // if DLIB_USE_BLAS
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// ------------------------------------------------------------------------------------
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/* Purpose */
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/* ======= */
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/* DTRSM solves one of the matrix equations */
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/* op( A )*X = alpha*B, or X*op( A ) = alpha*B, */
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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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/* op( A ) = A or op( A ) = A'. */
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/* The matrix X is overwritten on B. */
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/* Arguments */
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/* ========== */
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/* SIDE - 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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/* SIDE = 'L' or 'l' op( A )*X = alpha*B. */
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/* SIDE = 'R' or 'r' X*op( A ) = alpha*B. */
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/* Unchanged on exit. */
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/* UPLO - 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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/* UPLO = 'U' or 'u' A is an upper triangular matrix. */
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/* UPLO = 'L' or 'l' A is a lower triangular matrix. */
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/* Unchanged on exit. */
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/* TRANSA - 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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/* TRANSA = 'N' or 'n' op( A ) = A. */
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/* TRANSA = 'T' or 't' op( A ) = A'. */
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/* TRANSA = 'C' or 'c' op( A ) = A'. */
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/* Unchanged on exit. */
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/* DIAG - 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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/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */
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/* DIAG = 'N' or 'n' A is not assumed to be unit */
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/* triangular. */
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/* Unchanged on exit. */
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/* M - 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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/* N - 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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/* ALPHA - 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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/* Unchanged on exit. */
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/* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m */
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/* when SIDE = 'L' or 'l' and 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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/* Unchanged on exit. */
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/* LDA - 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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/* Unchanged on exit. */
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/* B - DOUBLE PRECISION array of 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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/* LDB - 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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/* Level 3 Blas routine. */
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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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template <typename T>
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void local_trsm(
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const CBLAS_ORDER Order,
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CBLAS_SIDE Side,
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CBLAS_UPLO Uplo,
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const CBLAS_TRANSPOSE TransA,
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const CBLAS_DIAG Diag,
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long m,
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long n,
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T alpha,
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const T *a,
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long lda,
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T *b,
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long ldb
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)
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/*!
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This is a copy of the dtrsm routine from the netlib.org BLAS which was run though
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f2c and converted into this form for use when a BLAS library is not available.
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!*/
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{
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if (Order == CblasRowMajor)
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{
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// since row major ordering looks like transposition to FORTRAN we need to flip a
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// few things.
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if (Side == CblasLeft)
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Side = CblasRight;
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else
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Side = CblasLeft;
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if (Uplo == CblasUpper)
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Uplo = CblasLower;
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else
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Uplo = CblasUpper;
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std::swap(m,n);
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}
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/* System generated locals */
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long a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
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/* Local variables */
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long i__, j, k, info;
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T temp;
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bool lside;
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long nrowa;
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bool upper;
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bool nounit;
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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 = (Side == CblasLeft);
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if (lside)
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{
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nrowa = m;
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} else
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{
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nrowa = n;
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}
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nounit = (Diag == CblasNonUnit);
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upper = (Uplo == CblasUpper);
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info = 0;
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if (! lside && ! (Side == CblasRight)) {
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info = 1;
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} else if (! upper && !(Uplo == CblasLower) ) {
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info = 2;
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} else if (!(TransA == CblasNoTrans) &&
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!(TransA == CblasTrans) &&
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!(TransA == CblasConjTrans)) {
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info = 3;
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} else if (!(Diag == CblasUnit) &&
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!(Diag == CblasNonUnit) ) {
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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 < std::max<long>(1,nrowa)) {
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info = 9;
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} else if (ldb < std::max<long>(1,m)) {
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info = 11;
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}
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DLIB_CASSERT( info == 0, "Invalid inputs given to local_trsm");
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/* Quick return if possible. */
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if (m == 0 || n == 0) {
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return;
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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;
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}
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/* Start the operations. */
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if (lside) {
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if (TransA == CblasNoTrans) {
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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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}
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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' )*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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i__2 = m;
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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];
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/* L110: */
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}
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if (nounit) {
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temp /= a[i__ + i__ * a_dim1];
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}
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b[i__ + j * b_dim1] = temp;
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/* L120: */
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}
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/* L130: */
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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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for (i__ = m; i__ >= 1; --i__) {
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temp = alpha * b[i__ + j * b_dim1];
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i__2 = m;
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for (k = i__ + 1; k <= i__2; ++k) {
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temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
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/* L140: */
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}
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if (nounit) {
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temp /= a[i__ + i__ * a_dim1];
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}
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b[i__ + j * b_dim1] = temp;
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/* L150: */
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}
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/* L160: */
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}
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}
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}
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} else {
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if (TransA == CblasNoTrans) {
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/* Form B := alpha*B*inv( A ). */
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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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/* L170: */
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}
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}
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i__2 = j - 1;
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for (k = 1; k <= i__2; ++k) {
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if (a[k + j * a_dim1] != 0.) {
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i__3 = m;
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for (i__ = 1; i__ <= i__3; ++i__) {
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b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
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i__ + k * b_dim1];
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/* L180: */
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}
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}
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/* L190: */
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}
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if (nounit) {
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temp = 1. / a[j + j * a_dim1];
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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] = temp * b[i__ + j * b_dim1];
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/* L200: */
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}
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}
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/* L210: */
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}
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} else {
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for (j = n; j >= 1; --j) {
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if (alpha != 1.) {
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i__1 = m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
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;
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/* L220: */
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}
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}
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i__1 = n;
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for (k = j + 1; k <= i__1; ++k) {
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if (a[k + j * a_dim1] != 0.) {
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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] -= a[k + j * a_dim1] * b[
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i__ + k * b_dim1];
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/* L230: */
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}
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}
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/* L240: */
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}
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if (nounit) {
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temp = 1. / a[j + j * a_dim1];
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i__1 = m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
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/* L250: */
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}
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}
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/* L260: */
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}
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}
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} else {
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/* Form B := alpha*B*inv( A' ). */
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if (upper) {
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for (k = n; k >= 1; --k) {
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if (nounit) {
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temp = 1. / a[k + k * a_dim1];
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i__1 = m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
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/* L270: */
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}
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}
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i__1 = k - 1;
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for (j = 1; j <= i__1; ++j) {
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if (a[j + k * a_dim1] != 0.) {
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temp = a[j + k * a_dim1];
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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] -= temp * b[i__ + k *
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b_dim1];
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/* L280: */
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}
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}
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/* L290: */
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}
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if (alpha != 1.) {
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i__1 = m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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b[i__ + k * b_dim1] = alpha * b[i__ + k * b_dim1]
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;
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/* L300: */
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}
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}
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/* L310: */
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}
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} else {
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i__1 = n;
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for (k = 1; k <= i__1; ++k) {
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if (nounit) {
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temp = 1. / a[k + k * a_dim1];
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i__2 = m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
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/* L320: */
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}
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}
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i__2 = n;
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for (j = k + 1; j <= i__2; ++j) {
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if (a[j + k * a_dim1] != 0.) {
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temp = a[j + k * a_dim1];
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i__3 = m;
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for (i__ = 1; i__ <= i__3; ++i__) {
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b[i__ + j * b_dim1] -= temp * b[i__ + k *
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b_dim1];
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/* L330: */
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}
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}
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/* L340: */
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}
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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__ + k * b_dim1] = alpha * b[i__ + k * b_dim1]
|
|
;
|
|
/* L350: */
|
|
}
|
|
}
|
|
/* L360: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// ------------------------------------------------------------------------------------
|
|
|
|
inline void cblas_trsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
|
|
const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
|
|
const CBLAS_DIAG Diag, const int M, const int N,
|
|
const float alpha, const float *A, const int lda,
|
|
float *B, const int ldb)
|
|
{
|
|
#ifdef DLIB_USE_BLAS
|
|
if (M > 4)
|
|
{
|
|
cblas_strsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
|
|
return;
|
|
}
|
|
#endif
|
|
local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
|
|
}
|
|
|
|
inline void cblas_trsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
|
|
const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
|
|
const CBLAS_DIAG Diag, const int M, const int N,
|
|
const double alpha, const double *A, const int lda,
|
|
double *B, const int ldb)
|
|
{
|
|
#ifdef DLIB_USE_BLAS
|
|
if (M > 4)
|
|
{
|
|
cblas_dtrsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
|
|
return;
|
|
}
|
|
#endif
|
|
local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
|
|
}
|
|
|
|
inline void cblas_trsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
|
|
const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
|
|
const CBLAS_DIAG Diag, const int M, const int N,
|
|
const long double alpha, const long double *A, const int lda,
|
|
long double *B, const int ldb)
|
|
{
|
|
local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
|
|
}
|
|
|
|
// ------------------------------------------------------------------------------------
|
|
|
|
template <
|
|
typename T,
|
|
long NR1, long NR2,
|
|
long NC1, long NC2,
|
|
typename MM
|
|
>
|
|
inline void triangular_solver (
|
|
const CBLAS_SIDE Side,
|
|
const CBLAS_UPLO Uplo,
|
|
const CBLAS_TRANSPOSE TransA,
|
|
const CBLAS_DIAG Diag,
|
|
const matrix<T,NR1,NC1,MM,row_major_layout>& A,
|
|
const T alpha,
|
|
matrix<T,NR2,NC2,MM,row_major_layout>& B
|
|
)
|
|
{
|
|
cblas_trsm(CblasRowMajor, Side, Uplo, TransA, Diag, B.nr(), B.nc(),
|
|
alpha, &A(0,0), A.nc(), &B(0,0), B.nc());
|
|
}
|
|
|
|
// ------------------------------------------------------------------------------------
|
|
|
|
template <
|
|
typename T,
|
|
long NR1, long NR2,
|
|
long NC1, long NC2,
|
|
typename MM
|
|
>
|
|
inline void triangular_solver (
|
|
const CBLAS_SIDE Side,
|
|
const CBLAS_UPLO Uplo,
|
|
const CBLAS_TRANSPOSE TransA,
|
|
const CBLAS_DIAG Diag,
|
|
const matrix<T,NR1,NC1,MM,column_major_layout>& A,
|
|
const T alpha,
|
|
matrix<T,NR2,NC2,MM,column_major_layout>& B
|
|
)
|
|
{
|
|
cblas_trsm(CblasColMajor, Side, Uplo, TransA, Diag, B.nr(), B.nc(),
|
|
alpha, &A(0,0), A.nr(), &B(0,0), B.nr());
|
|
}
|
|
|
|
// ------------------------------------------------------------------------------------
|
|
|
|
template <
|
|
typename T,
|
|
long NR1, long NR2,
|
|
long NC1, long NC2,
|
|
typename MM
|
|
>
|
|
inline void triangular_solver (
|
|
const CBLAS_SIDE Side,
|
|
const CBLAS_UPLO Uplo,
|
|
const CBLAS_TRANSPOSE TransA,
|
|
const CBLAS_DIAG Diag,
|
|
const matrix<T,NR1,NC1,MM,column_major_layout>& A,
|
|
matrix<T,NR2,NC2,MM,column_major_layout>& B,
|
|
long rows_of_B
|
|
)
|
|
{
|
|
const T alpha = 1;
|
|
cblas_trsm(CblasColMajor, Side, Uplo, TransA, Diag, rows_of_B, B.nc(),
|
|
alpha, &A(0,0), A.nr(), &B(0,0), B.nr());
|
|
}
|
|
|
|
// ------------------------------------------------------------------------------------
|
|
|
|
template <
|
|
typename T,
|
|
long NR1, long NR2,
|
|
long NC1, long NC2,
|
|
typename MM,
|
|
typename layout
|
|
>
|
|
inline void triangular_solver (
|
|
const CBLAS_SIDE Side,
|
|
const CBLAS_UPLO Uplo,
|
|
const CBLAS_TRANSPOSE TransA,
|
|
const CBLAS_DIAG Diag,
|
|
const matrix<T,NR1,NC1,MM,layout>& A,
|
|
matrix<T,NR2,NC2,MM,layout>& B
|
|
)
|
|
{
|
|
const T alpha = 1;
|
|
triangular_solver(Side, Uplo, TransA, Diag, A, alpha, B);
|
|
}
|
|
|
|
// ------------------------------------------------------------------------------------
|
|
|
|
}
|
|
}
|
|
|
|
#endif // DLIB_MATRiX_TRSM_Hh_
|
|
|