LAPACK
3.4.2
LAPACK: Linear Algebra PACKage
|
Functions/Subroutines | |
subroutine | sgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) |
SGBMV | |
subroutine | sgemv (TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) |
SGEMV | |
subroutine | sger (M, N, ALPHA, X, INCX, Y, INCY, A, LDA) |
SGER | |
subroutine | ssbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) |
SSBMV | |
subroutine | sspmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY) |
SSPMV | |
subroutine | sspr (UPLO, N, ALPHA, X, INCX, AP) |
SSPR | |
subroutine | sspr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, AP) |
SSPR2 | |
subroutine | ssymv (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) |
SSYMV | |
subroutine | ssyr (UPLO, N, ALPHA, X, INCX, A, LDA) |
SSYR | |
subroutine | ssyr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA) |
SSYR2 | |
subroutine | stbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) |
STBMV | |
subroutine | stbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) |
STBSV | |
subroutine | stpmv (UPLO, TRANS, DIAG, N, AP, X, INCX) |
STPMV | |
subroutine | stpsv (UPLO, TRANS, DIAG, N, AP, X, INCX) |
STPSV | |
subroutine | strmv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) |
STRMV | |
subroutine | strsv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) |
STRSV |
This is the group of real LEVEL 2 BLAS routines.
subroutine sgbmv | ( | character | TRANS, |
integer | M, | ||
integer | N, | ||
integer | KL, | ||
integer | KU, | ||
real | ALPHA, | ||
real, dimension(lda,*) | A, | ||
integer | LDA, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real | BETA, | ||
real, dimension(*) | Y, | ||
integer | INCY | ||
) |
SGBMV
SGBMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.
[in] | TRANS | TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. |
[in] | M | M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. |
[in] | N | N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. |
[in] | KL | KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. |
[in] | KU | KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. |
[in] | ALPHA | ALPHA is REAL On entry, ALPHA specifies the scalar alpha. |
[in] | A | A is REAL array of DIMENSION ( LDA, n ). Before entry, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE |
[in] | LDA | LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( kl + ku + 1 ). |
[in] | X | X is REAL array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in] | BETA | BETA is REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[in,out] | Y | Y is REAL array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. |
[in] | INCY | INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. |
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 186 of file sgbmv.f.
subroutine sgemv | ( | character | TRANS, |
integer | M, | ||
integer | N, | ||
real | ALPHA, | ||
real, dimension(lda,*) | A, | ||
integer | LDA, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real | BETA, | ||
real, dimension(*) | Y, | ||
integer | INCY | ||
) |
SGEMV
SGEMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.
[in] | TRANS | TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. |
[in] | M | M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. |
[in] | N | N is INTEGER On entry, N specifies the number of columns of the matrix A. 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, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. |
[in] | LDA | LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). |
[in] | X | X is REAL array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in] | BETA | BETA is REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[in,out] | Y | Y is REAL array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. |
[in] | INCY | INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. |
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 157 of file sgemv.f.
subroutine sger | ( | integer | M, |
integer | N, | ||
real | ALPHA, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real, dimension(*) | Y, | ||
integer | INCY, | ||
real, dimension(lda,*) | A, | ||
integer | LDA | ||
) |
SGER
SGER performs the rank 1 operation A := alpha*x*y**T + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.
[in] | M | M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. |
[in] | N | N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. |
[in] | ALPHA | ALPHA is REAL On entry, ALPHA specifies the scalar alpha. |
[in] | X | X is REAL array of dimension at least ( 1 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m element vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in] | Y | Y is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. |
[in] | INCY | INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. |
[in,out] | A | A is REAL array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix. |
[in] | LDA | LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). |
Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 131 of file sger.f.
subroutine ssbmv | ( | character | UPLO, |
integer | N, | ||
integer | K, | ||
real | ALPHA, | ||
real, dimension(lda,*) | A, | ||
integer | LDA, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real | BETA, | ||
real, dimension(*) | Y, | ||
integer | INCY | ||
) |
SSBMV
SSBMV performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric band matrix, with k super-diagonals.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied as follows: UPLO = 'U' or 'u' The upper triangular part of A is being supplied. UPLO = 'L' or 'l' The lower triangular part of A is being supplied. |
[in] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | K | K is INTEGER On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K. |
[in] | ALPHA | ALPHA is REAL On entry, ALPHA specifies the scalar alpha. |
[in] | A | A is REAL array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the symmetric matrix, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer the upper triangular part of a symmetric band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the symmetric matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer the lower triangular part of a symmetric band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE |
[in] | LDA | LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ). |
[in] | X | X is REAL array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in] | BETA | BETA is REAL On entry, BETA specifies the scalar beta. |
[in,out] | Y | Y is REAL array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. |
[in] | INCY | INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. |
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 185 of file ssbmv.f.
subroutine sspmv | ( | character | UPLO, |
integer | N, | ||
real | ALPHA, | ||
real, dimension(*) | AP, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real | BETA, | ||
real, dimension(*) | Y, | ||
integer | INCY | ||
) |
SSPMV
SSPMV performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP. |
[in] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | ALPHA | ALPHA is REAL On entry, ALPHA specifies the scalar alpha. |
[in] | AP | AP is REAL array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. |
[in] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in] | BETA | BETA is REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[in,out] | Y | Y is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. |
[in] | INCY | INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. |
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 148 of file sspmv.f.
subroutine sspr | ( | character | UPLO, |
integer | N, | ||
real | ALPHA, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real, dimension(*) | AP | ||
) |
SSPR
SSPR performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix, supplied in packed form.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP. |
[in] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | ALPHA | ALPHA is REAL On entry, ALPHA specifies the scalar alpha. |
[in] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in,out] | AP | AP is REAL array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP is overwritten by the lower triangular part of the updated matrix. |
Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 128 of file sspr.f.
subroutine sspr2 | ( | character | UPLO, |
integer | N, | ||
real | ALPHA, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real, dimension(*) | Y, | ||
integer | INCY, | ||
real, dimension(*) | AP | ||
) |
SSPR2
SSPR2 performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP. |
[in] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | ALPHA | ALPHA is REAL On entry, ALPHA specifies the scalar alpha. |
[in] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in] | Y | Y is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. |
[in] | INCY | INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. |
[in,out] | AP | AP is REAL array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP is overwritten by the lower triangular part of the updated matrix. |
Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 143 of file sspr2.f.
subroutine ssymv | ( | character | UPLO, |
integer | N, | ||
real | ALPHA, | ||
real, dimension(lda,*) | A, | ||
integer | LDA, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real | BETA, | ||
real, dimension(*) | Y, | ||
integer | INCY | ||
) |
SSYMV
SSYMV performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. |
[in] | N | N is INTEGER On entry, N specifies the order of the matrix A. 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, n ). Before entry with 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. Before entry with 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. LDA must be at least max( 1, n ). |
[in] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in] | BETA | BETA is REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[in,out] | Y | Y is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. |
[in] | INCY | INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. |
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 153 of file ssymv.f.
subroutine ssyr | ( | character | UPLO, |
integer | N, | ||
real | ALPHA, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real, dimension(lda,*) | A, | ||
integer | LDA | ||
) |
SSYR
SSYR performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. |
[in] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | ALPHA | ALPHA is REAL On entry, ALPHA specifies the scalar alpha. |
[in] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in,out] | A | A is REAL array of DIMENSION ( LDA, n ). Before entry with 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. On exit, the upper triangular part of the array A 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 A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. |
[in] | LDA | LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). |
Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 133 of file ssyr.f.
subroutine ssyr2 | ( | character | UPLO, |
integer | N, | ||
real | ALPHA, | ||
real, dimension(*) | X, | ||
integer | INCX, | ||
real, dimension(*) | Y, | ||
integer | INCY, | ||
real, dimension(lda,*) | A, | ||
integer | LDA | ||
) |
SSYR2
SSYR2 performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. |
[in] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | ALPHA | ALPHA is REAL On entry, ALPHA specifies the scalar alpha. |
[in] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
[in] | Y | Y is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. |
[in] | INCY | INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. |
[in,out] | A | A is REAL array of DIMENSION ( LDA, n ). Before entry with 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. On exit, the upper triangular part of the array A 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 A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. |
[in] | LDA | LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). |
Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 148 of file ssyr2.f.
subroutine stbmv | ( | character | UPLO, |
character | TRANS, | ||
character | DIAG, | ||
integer | N, | ||
integer | K, | ||
real, dimension(lda,*) | A, | ||
integer | LDA, | ||
real, dimension(*) | X, | ||
integer | INCX | ||
) |
STBMV
STBMV performs one of the matrix-vector operations x := A*x, or x := A**T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix 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] | TRANS | TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A**T*x. TRANS = 'C' or 'c' x := A**T*x. |
[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] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | K | K is INTEGER On entry with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K. |
[in] | A | A is REAL array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer an upper triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, 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. LDA must be at least ( k + 1 ). |
[in,out] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the tranformed vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 187 of file stbmv.f.
subroutine stbsv | ( | character | UPLO, |
character | TRANS, | ||
character | DIAG, | ||
integer | N, | ||
integer | K, | ||
real, dimension(lda,*) | A, | ||
integer | LDA, | ||
real, dimension(*) | X, | ||
integer | INCX | ||
) |
STBSV
STBSV solves one of the systems of equations A*x = b, or A**T*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix 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] | TRANS | TRANS is CHARACTER*1 On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A**T*x = b. TRANS = 'C' or 'c' A**T*x = b. |
[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] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | K | K is INTEGER On entry with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K. |
[in] | A | A is REAL array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer an upper triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, 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. LDA must be at least ( k + 1 ). |
[in,out] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 190 of file stbsv.f.
subroutine stpmv | ( | character | UPLO, |
character | TRANS, | ||
character | DIAG, | ||
integer | N, | ||
real, dimension(*) | AP, | ||
real, dimension(*) | X, | ||
integer | INCX | ||
) |
STPMV
STPMV performs one of the matrix-vector operations x := A*x, or x := A**T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix 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] | TRANS | TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A**T*x. TRANS = 'C' or 'c' x := A**T*x. |
[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] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | AP | AP is REAL array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity. |
[in,out] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the tranformed vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 143 of file stpmv.f.
subroutine stpsv | ( | character | UPLO, |
character | TRANS, | ||
character | DIAG, | ||
integer | N, | ||
real, dimension(*) | AP, | ||
real, dimension(*) | X, | ||
integer | INCX | ||
) |
STPSV
STPSV solves one of the systems of equations A*x = b, or A**T*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix 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] | TRANS | TRANS is CHARACTER*1 On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A**T*x = b. TRANS = 'C' or 'c' A**T*x = b. |
[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] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | AP | AP is REAL array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity. |
[in,out] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 145 of file stpsv.f.
subroutine strmv | ( | character | UPLO, |
character | TRANS, | ||
character | DIAG, | ||
integer | N, | ||
real, dimension(lda,*) | A, | ||
integer | LDA, | ||
real, dimension(*) | X, | ||
integer | INCX | ||
) |
STRMV
STRMV performs one of the matrix-vector operations x := A*x, or x := A**T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix 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] | TRANS | TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A**T*x. TRANS = 'C' or 'c' x := A**T*x. |
[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] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | A | A is REAL array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n 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 n by n 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. LDA must be at least max( 1, n ). |
[in,out] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the tranformed vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 148 of file strmv.f.
subroutine strsv | ( | character | UPLO, |
character | TRANS, | ||
character | DIAG, | ||
integer | N, | ||
real, dimension(lda,*) | A, | ||
integer | LDA, | ||
real, dimension(*) | X, | ||
integer | INCX | ||
) |
STRSV
STRSV solves one of the systems of equations A*x = b, or A**T*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.
[in] | UPLO | UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix 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] | TRANS | TRANS is CHARACTER*1 On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A**T*x = b. TRANS = 'C' or 'c' A**T*x = b. |
[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] | N | N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. |
[in] | A | A is REAL array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n 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 n by n 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. LDA must be at least max( 1, n ). |
[in,out] | X | X is REAL array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. |
Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 150 of file strsv.f.