.TH "double_blas_level3" 3 "Sun Nov 27 2022" "Version 3.11.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME double_blas_level3 \- double .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBdgemm\fP (TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)" .br .RI "\fBDGEMM\fP " .ti -1c .RI "subroutine \fBdsymm\fP (SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)" .br .RI "\fBDSYMM\fP " .ti -1c .RI "subroutine \fBdsyr2k\fP (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)" .br .RI "\fBDSYR2K\fP " .ti -1c .RI "subroutine \fBdsyrk\fP (UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)" .br .RI "\fBDSYRK\fP " .ti -1c .RI "subroutine \fBdtrmm\fP (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)" .br .RI "\fBDTRMM\fP " .ti -1c .RI "subroutine \fBdtrsm\fP (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)" .br .RI "\fBDTRSM\fP " .in -1c .SH "Detailed Description" .PP This is the group of double LEVEL 3 BLAS routines\&. .SH "Function Documentation" .PP .SS "subroutine dgemm (character TRANSA, character TRANSB, integer M, integer N, integer K, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB, double precision BETA, double precision, dimension(ldc,*) C, integer LDC)" .PP \fBDGEMM\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DGEMM performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = X**T, alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANSA\fP .PP .nf TRANSA is CHARACTER*1 On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n', op( A ) = A\&. TRANSA = 'T' or 't', op( A ) = A**T\&. TRANSA = 'C' or 'c', op( A ) = A**T\&. .fi .PP .br \fITRANSB\fP .PP .nf TRANSB is CHARACTER*1 On entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B\&. TRANSB = 'T' or 't', op( B ) = B**T\&. TRANSB = 'C' or 'c', op( B ) = B**T\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIK\fP .PP .nf K is INTEGER On entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( B )\&. K must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION\&. On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is k when TRANSA = 'N' or 'n', and is m otherwise\&. Before entry with TRANSA = 'N' or 'n', the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When TRANSA = 'N' or 'n' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k )\&. .fi .PP .br \fIB\fP .PP .nf B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is n when TRANSB = 'N' or 'n', and is k otherwise\&. Before entry with TRANSB = 'N' or 'n', the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k part of the array B must contain the matrix B\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. When TRANSB = 'N' or 'n' then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n )\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is DOUBLE PRECISION\&. On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then C need not be set on input\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension ( LDC, N ) Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry\&. On exit, the array C is overwritten by the m by n matrix ( alpha*op( A )*op( B ) + beta*C )\&. .fi .PP .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, m )\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SS "subroutine dsymm (character SIDE, character UPLO, integer M, integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB, double precision BETA, double precision, dimension(ldc,*) C, integer LDC)" .PP \fBDSYMM\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSYMM performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fISIDE\fP .PP .nf SIDE is CHARACTER*1 On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation as follows: SIDE = 'L' or 'l' C := alpha*A*B + beta*C, SIDE = 'R' or 'r' C := alpha*B*A + beta*C, .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of the symmetric matrix is to be referenced\&. UPLO = 'L' or 'l' Only the lower triangular part of the symmetric matrix is to be referenced\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of the matrix C\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION\&. On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is m when SIDE = 'L' or 'l' and is n otherwise\&. Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading m by m lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced\&. Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n )\&. .fi .PP .br \fIB\fP .PP .nf B is DOUBLE PRECISION array, dimension ( LDB, N ) Before entry, the leading m by n part of the array B must contain the matrix B\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. LDB must be at least max( 1, m )\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is DOUBLE PRECISION\&. On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then C need not be set on input\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension ( LDC, N ) Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry\&. On exit, the array C is overwritten by the m by n updated matrix\&. .fi .PP .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, m )\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SS "subroutine dsyr2k (character UPLO, character TRANS, integer N, integer K, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB, double precision BETA, double precision, dimension(ldc,*) C, integer LDC)" .PP \fBDSYR2K\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSYR2K performs one of the symmetric rank 2k operations C := alpha*A*B**T + alpha*B*A**T + beta*C, or C := alpha*A**T*B + alpha*B**T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced\&. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced\&. .fi .PP .br \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + beta*C\&. TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + beta*C\&. TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + beta*C\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIK\fP .PP .nf K is INTEGER On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrices A and B\&. K must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION\&. On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k )\&. .fi .PP .br \fIB\fP .PP .nf B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k )\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is DOUBLE PRECISION\&. On entry, BETA specifies the scalar beta\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension ( LDC, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced\&. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix\&. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced\&. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix\&. .fi .PP .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, n )\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SS "subroutine dsyrk (character UPLO, character TRANS, integer N, integer K, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision BETA, double precision, dimension(ldc,*) C, integer LDC)" .PP \fBDSYRK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSYRK performs one of the symmetric rank k operations C := alpha*A*A**T + beta*C, or C := alpha*A**T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced\&. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced\&. .fi .PP .br \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C\&. TRANS = 'T' or 't' C := alpha*A**T*A + beta*C\&. TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIK\fP .PP .nf K is INTEGER On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrix A, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrix A\&. K must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION\&. On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k )\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is DOUBLE PRECISION\&. On entry, BETA specifies the scalar beta\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension ( LDC, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced\&. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix\&. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced\&. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix\&. .fi .PP .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, n )\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SS "subroutine dtrmm (character SIDE, character UPLO, character TRANSA, character DIAG, integer M, integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB)" .PP \fBDTRMM\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DTRMM performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ), where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A**T\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fISIDE\fP .PP .nf SIDE is CHARACTER*1 On entry, SIDE specifies whether op( A ) multiplies B from the left or right as follows: SIDE = 'L' or 'l' B := alpha*op( A )*B\&. SIDE = 'R' or 'r' B := alpha*B*op( A )\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix\&. UPLO = 'L' or 'l' A is a lower triangular matrix\&. .fi .PP .br \fITRANSA\fP .PP .nf TRANSA is CHARACTER*1 On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A\&. TRANSA = 'T' or 't' op( A ) = A**T\&. TRANSA = 'C' or 'c' op( A ) = A**T\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular\&. DIAG = 'N' or 'n' A is not assumed to be unit triangular\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of B\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of B\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION\&. On entry, ALPHA specifies the scalar alpha\&. When alpha is zero then A is not referenced and B need not be set before entry\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'\&. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced\&. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced\&. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n )\&. .fi .PP .br \fIB\fP .PP .nf B is DOUBLE PRECISION array, dimension ( LDB, N ) Before entry, the leading m by n part of the array B must contain the matrix B, and on exit is overwritten by the transformed matrix\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. LDB must be at least max( 1, m )\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SS "subroutine dtrsm (character SIDE, character UPLO, character TRANSA, character DIAG, integer M, integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB)" .PP \fBDTRSM\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DTRSM solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A**T\&. The matrix X is overwritten on B\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fISIDE\fP .PP .nf SIDE is CHARACTER*1 On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = 'L' or 'l' op( A )*X = alpha*B\&. SIDE = 'R' or 'r' X*op( A ) = alpha*B\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix\&. UPLO = 'L' or 'l' A is a lower triangular matrix\&. .fi .PP .br \fITRANSA\fP .PP .nf TRANSA is CHARACTER*1 On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A\&. TRANSA = 'T' or 't' op( A ) = A**T\&. TRANSA = 'C' or 'c' op( A ) = A**T\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular\&. DIAG = 'N' or 'n' A is not assumed to be unit triangular\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of B\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of B\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION\&. On entry, ALPHA specifies the scalar alpha\&. When alpha is zero then A is not referenced and B need not be set before entry\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m when SIDE = 'L' or 'l' and k is n when SIDE = 'R' or 'r'\&. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced\&. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced\&. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n )\&. .fi .PP .br \fIB\fP .PP .nf B is DOUBLE PRECISION array, dimension ( LDB, N ) Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. LDB must be at least max( 1, m )\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Level 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.