--- name: "gemm" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/gemm" --- # gemm(3) gemm: general matrix-matrix multiply ## NAME gemm - gemm: general matrix-matrix multiply ## SYNOPSIS ### Functions subroutine **cgemm** (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)\ **CGEMM** subroutine **dgemm** (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)\ **DGEMM** subroutine **sgemm** (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)\ **SGEMM** subroutine **zgemm** (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)\ **ZGEMM** ## Detailed Description ## Function Documentation ### subroutine cgemm (character transa, character transb, integer m, integer n, integer k, complex alpha, complex, dimension(lda,\*) a, integer lda, complex, dimension(ldb,\*) b, integer ldb, complex beta, complex, dimension(ldc,\*) c, integer ldc) **CGEMM** **Purpose:** ``` !> !> CGEMM 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 or op( X ) = X**H, !> !> 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**H. !> ``` *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**H. !> ``` *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 COMPLEX !> On entry, ALPHA specifies the scalar alpha. !> ``` *A* ``` !> A is COMPLEX 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 COMPLEX 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 COMPLEX !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then C need not be set on input. !> ``` *C* ``` !> C is COMPLEX 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. !> ``` Definition at line **186** of file **cgemm.f**. ### 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. !> ``` Definition at line **186** of file **dgemm.f**. ### subroutine sgemm (character transa, character transb, integer m, integer n, integer k, real alpha, real, dimension(lda,\*) a, integer lda, real, dimension(ldb,\*) b, integer ldb, real beta, real, dimension(ldc,\*) c, integer ldc) **SGEMM** **Purpose:** ``` !> !> SGEMM 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 REAL !> On entry, ALPHA specifies the scalar alpha. !> ``` *A* ``` !> A is REAL 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 REAL 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 REAL !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then C need not be set on input. !> ``` *C* ``` !> C is REAL 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. !> ``` Definition at line **186** of file **sgemm.f**. ### subroutine zgemm (character transa, character transb, integer m, integer n, integer k, complex\*16 alpha, complex\*16, dimension(lda,\*) a, integer lda, complex\*16, dimension(ldb,\*) b, integer ldb, complex\*16 beta, complex\*16, dimension(ldc,\*) c, integer ldc) **ZGEMM** **Purpose:** ``` !> !> ZGEMM 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 or op( X ) = X**H, !> !> 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**H. !> ``` *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**H. !> ``` *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 COMPLEX*16 !> On entry, ALPHA specifies the scalar alpha. !> ``` *A* ``` !> A is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then C need not be set on input. !> ``` *C* ``` !> C is COMPLEX*16 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. !> ``` Definition at line **186** of file **zgemm.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.