--- name: "double_blas_level3" section: "3" platform: "linux" package: "liblapack-doc" version: "3.11.0-2" release: "Debian 12 (Bookworm)" platforms: ["linux"] url: "https://new.carta.tech/double_blas_level3" --- # double\_blas\_level3(3) double ## NAME double\_blas\_level3 - double ## SYNOPSIS ### Functions subroutine **dgemm** (TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)\ **DGEMM** subroutine **dsymm** (SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)\ **DSYMM** subroutine **dsyr2k** (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)\ **DSYR2K** subroutine **dsyrk** (UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)\ **DSYRK** subroutine **dtrmm** (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)\ **DTRMM** subroutine **dtrsm** (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)\ **DTRSM** ## Detailed Description This is the group of double LEVEL 3 BLAS routines. ## Function Documentation ### 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) **DGEMM** **Purpose:** ``` 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. ``` **Parameters** *TRANSA* ``` 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. ``` *TRANSB* ``` 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. ``` *M* ``` 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. ``` *N* ``` 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. ``` *K* ``` 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. ``` *ALPHA* ``` ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. ``` *A* ``` 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. ``` *LDA* ``` 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 ). ``` *B* ``` 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. ``` *LDB* ``` 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 ). ``` *BETA* ``` 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. ``` *C* ``` 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 ). ``` *LDC* ``` 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 ). ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` 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. ``` ### 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) **DSYMM** **Purpose:** ``` 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. ``` **Parameters** *SIDE* ``` 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, ``` *UPLO* ``` 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. ``` *M* ``` M is INTEGER On entry, M specifies the number of rows of the matrix C. M must be at least zero. ``` *N* ``` N is INTEGER On entry, N specifies the number of columns of the matrix C. N must be at least zero. ``` *ALPHA* ``` ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. ``` *A* ``` 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. ``` *LDA* ``` 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 ). ``` *B* ``` 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. ``` *LDB* ``` 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 ). ``` *BETA* ``` 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. ``` *C* ``` 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. ``` *LDC* ``` 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 ). ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` 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. ``` ### 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) **DSYR2K** **Purpose:** ``` 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. ``` **Parameters** *UPLO* ``` 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. ``` *TRANS* ``` 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. ``` *N* ``` N is INTEGER On entry, N specifies the order of the matrix C. N must be at least zero. ``` *K* ``` 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. ``` *ALPHA* ``` ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. ``` *A* ``` 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. ``` *LDA* ``` 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 ). ``` *B* ``` 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. ``` *LDB* ``` 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 ). ``` *BETA* ``` BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. ``` *C* ``` 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. ``` *LDC* ``` 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 ). ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` 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. ``` ### 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) **DSYRK** **Purpose:** ``` 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. ``` **Parameters** *UPLO* ``` 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. ``` *TRANS* ``` 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. ``` *N* ``` N is INTEGER On entry, N specifies the order of the matrix C. N must be at least zero. ``` *K* ``` 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. ``` *ALPHA* ``` ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. ``` *A* ``` 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. ``` *LDA* ``` 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 ). ``` *BETA* ``` BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. ``` *C* ``` 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. ``` *LDC* ``` 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 ). ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` 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. ``` ### 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) **DTRMM** **Purpose:** ``` 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. ``` **Parameters** *SIDE* ``` 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 ). ``` *UPLO* ``` 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. ``` *TRANSA* ``` 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. ``` *DIAG* ``` 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. ``` *M* ``` M is INTEGER On entry, M specifies the number of rows of B. M must be at least zero. ``` *N* ``` N is INTEGER On entry, N specifies the number of columns of B. N must be at least zero. ``` *ALPHA* ``` 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. ``` *A* ``` 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. ``` *LDA* ``` 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 ). ``` *B* ``` 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. ``` *LDB* ``` 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 ). ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` 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. ``` ### 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) **DTRSM** **Purpose:** ``` 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. ``` **Parameters** *SIDE* ``` 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. ``` *UPLO* ``` 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. ``` *TRANSA* ``` 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. ``` *DIAG* ``` 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. ``` *M* ``` M is INTEGER On entry, M specifies the number of rows of B. M must be at least zero. ``` *N* ``` N is INTEGER On entry, N specifies the number of columns of B. N must be at least zero. ``` *ALPHA* ``` 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. ``` *A* ``` 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. ``` *LDA* ``` 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 ). ``` *B* ``` 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. ``` *LDB* ``` 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 ). ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` 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. ``` ## Author Generated automatically by Doxygen for LAPACK from the source code.