LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  sgemm (TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC) 
SGEMM  
subroutine  ssymm (SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC) 
SSYMM  
subroutine  ssyr2k (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC) 
SSYR2K  
subroutine  ssyrk (UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC) 
SSYRK  
subroutine  strmm (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB) 
STRMM  
subroutine  strsm (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB) 
STRSM 
This is the group of real LEVEL 3 BLAS routines.
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
SGEMM performs one of the matrixmatrix 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.
[in]  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. 
[in]  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. 
[in]  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. 
[in]  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. 
[in]  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. 
[in]  ALPHA  ALPHA is REAL On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is REAL array of 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. 
[in]  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 ). 
[in]  B  B is REAL array of 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. 
[in]  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 ). 
[in]  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. 
[in,out]  C  C is REAL array of 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 ). 
[in]  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 ). 
Level 3 Blas routine.  Written on 8February1989. 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 188 of file sgemm.f.
subroutine ssymm  (  character  SIDE, 
character  UPLO,  
integer  M,  
integer  N,  
real  ALPHA,  
real, dimension(lda,*)  A,  
integer  LDA,  
real, dimension(ldb,*)  B,  
integer  LDB,  
real  BETA,  
real, dimension(ldc,*)  C,  
integer  LDC  
) 
SSYMM
SSYMM performs one of the matrixmatrix 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.
[in]  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, 
[in]  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. 
[in]  M  M is INTEGER On entry, M specifies the number of rows of the matrix C. M must be at least zero. 
[in]  N  N is INTEGER On entry, N specifies the number of columns of the matrix C. N must be at least zero. 
[in]  ALPHA  ALPHA is REAL On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is REAL array of 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. 
[in]  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 ). 
[in]  B  B is REAL array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B. 
[in]  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 ). 
[in]  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. 
[in,out]  C  C is REAL array of 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. 
[in]  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 ). 
Level 3 Blas routine.  Written on 8February1989. 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 190 of file ssymm.f.
subroutine ssyr2k  (  character  UPLO, 
character  TRANS,  
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  
) 
SSYR2K
SSYR2K 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.
[in]  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. 
[in]  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. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix C. N must be at least zero. 
[in]  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. 
[in]  ALPHA  ALPHA is REAL On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is REAL array of 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. 
[in]  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 ). 
[in]  B  B is REAL array of 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. 
[in]  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 ). 
[in]  BETA  BETA is REAL On entry, BETA specifies the scalar beta. 
[in,out]  C  C is REAL array of 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. 
[in]  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 ). 
Level 3 Blas routine.  Written on 8February1989. 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 193 of file ssyr2k.f.
subroutine ssyrk  (  character  UPLO, 
character  TRANS,  
integer  N,  
integer  K,  
real  ALPHA,  
real, dimension(lda,*)  A,  
integer  LDA,  
real  BETA,  
real, dimension(ldc,*)  C,  
integer  LDC  
) 
SSYRK
SSYRK 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.
[in]  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. 
[in]  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. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix C. N must be at least zero. 
[in]  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. 
[in]  ALPHA  ALPHA is REAL On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is REAL array of 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. 
[in]  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 ). 
[in]  BETA  BETA is REAL On entry, BETA specifies the scalar beta. 
[in,out]  C  C is REAL array of 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. 
[in]  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 ). 
Level 3 Blas routine.  Written on 8February1989. 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 170 of file ssyrk.f.
subroutine strmm  (  character  SIDE, 
character  UPLO,  
character  TRANSA,  
character  DIAG,  
integer  M,  
integer  N,  
real  ALPHA,  
real, dimension(lda,*)  A,  
integer  LDA,  
real, dimension(ldb,*)  B,  
integer  LDB  
) 
STRMM
STRMM performs one of the matrixmatrix 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 nonunit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A**T.
[in]  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 ). 
[in]  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. 
[in]  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. 
[in]  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. 
[in]  M  M is INTEGER On entry, M specifies the number of rows of B. M must be at least zero. 
[in]  N  N is INTEGER On entry, N specifies the number of columns of B. N must be at least zero. 
[in]  ALPHA  ALPHA is REAL On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. 
[in]  A  A is REAL array of 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. 
[in]  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 ). 
[in,out]  B  B is REAL array of 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. 
[in]  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 ). 
Level 3 Blas routine.  Written on 8February1989. 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 178 of file strmm.f.
subroutine strsm  (  character  SIDE, 
character  UPLO,  
character  TRANSA,  
character  DIAG,  
integer  M,  
integer  N,  
real  ALPHA,  
real, dimension(lda,*)  A,  
integer  LDA,  
real, dimension(ldb,*)  B,  
integer  LDB  
) 
STRSM
STRSM 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 nonunit, 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.
[in]  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. 
[in]  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. 
[in]  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. 
[in]  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. 
[in]  M  M is INTEGER On entry, M specifies the number of rows of B. M must be at least zero. 
[in]  N  N is INTEGER On entry, N specifies the number of columns of B. N must be at least zero. 
[in]  ALPHA  ALPHA is REAL On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. 
[in]  A  A is REAL array of 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. 
[in]  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 ). 
[in,out]  B  B is REAL array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the righthand side matrix B, and on exit is overwritten by the solution matrix X. 
[in]  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 ). 
Level 3 Blas routine.  Written on 8February1989. 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 182 of file strsm.f.