LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  dgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
DGBMV  
subroutine  dgemv (TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
DGEMV  
subroutine  dger (M, N, ALPHA, X, INCX, Y, INCY, A, LDA) 
DGER  
subroutine  dsbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
DSBMV  
subroutine  dspmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY) 
DSPMV  
subroutine  dspr (UPLO, N, ALPHA, X, INCX, AP) 
DSPR  
subroutine  dspr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, AP) 
DSPR2  
subroutine  dsymv (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
DSYMV  
subroutine  dsyr (UPLO, N, ALPHA, X, INCX, A, LDA) 
DSYR  
subroutine  dsyr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA) 
DSYR2  
subroutine  dtbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) 
DTBMV  
subroutine  dtbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) 
DTBSV  
subroutine  dtpmv (UPLO, TRANS, DIAG, N, AP, X, INCX) 
DTPMV  
subroutine  dtpsv (UPLO, TRANS, DIAG, N, AP, X, INCX) 
DTPSV  
subroutine  dtrmv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) 
DTRMV 
This is the group of double LEVEL 2 BLAS routines.
subroutine dgbmv  (  character  TRANS, 
integer  M,  
integer  N,  
integer  KL,  
integer  KU,  
double precision  ALPHA,  
double precision, dimension(lda,*)  A,  
integer  LDA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision  BETA,  
double precision, dimension(*)  Y,  
integer  INCY  
) 
DGBMV
DGBMV performs one of the matrixvector 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 subdiagonals and ku superdiagonals.
[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 subdiagonals of the matrix A. KL must satisfy 0 .le. KL. 
[in]  KU  KU is INTEGER On entry, KU specifies the number of superdiagonals of the matrix A. KU must satisfy 0 .le. KU. 
[in]  ALPHA  ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is DOUBLE PRECISION 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 superdiagonal starting at position 2 in row ku, the first subdiagonal 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 DOUBLE PRECISION 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 DOUBLE PRECISION. 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 DOUBLE PRECISION 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 22October1986. 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 dgbmv.f.
subroutine dgemv  (  character  TRANS, 
integer  M,  
integer  N,  
double precision  ALPHA,  
double precision, dimension(lda,*)  A,  
integer  LDA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision  BETA,  
double precision, dimension(*)  Y,  
integer  INCY  
) 
DGEMV
DGEMV performs one of the matrixvector 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION. 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 DOUBLE PRECISION 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 nonzero, 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 22October1986. 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 dgemv.f.
subroutine dger  (  integer  M, 
integer  N,  
double precision  ALPHA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision, dimension(*)  Y,  
integer  INCY,  
double precision, dimension(lda,*)  A,  
integer  LDA  
) 
DGER
DGER 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 22October1986. 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 dger.f.
subroutine dsbmv  (  character  UPLO, 
integer  N,  
integer  K,  
double precision  ALPHA,  
double precision, dimension(lda,*)  A,  
integer  LDA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision  BETA,  
double precision, dimension(*)  Y,  
integer  INCY  
) 
DSBMV
DSBMV performs the matrixvector 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 superdiagonals.
[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 superdiagonals of the matrix A. K must satisfy 0 .le. K. 
[in]  ALPHA  ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is DOUBLE PRECISION 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 superdiagonal 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 subdiagonal 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 DOUBLE PRECISION 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 DOUBLE PRECISION. On entry, BETA specifies the scalar beta. 
[in,out]  Y  Y is DOUBLE PRECISION 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 22October1986. 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 dsbmv.f.
subroutine dspmv  (  character  UPLO, 
integer  N,  
double precision  ALPHA,  
double precision, dimension(*)  AP,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision  BETA,  
double precision, dimension(*)  Y,  
integer  INCY  
) 
DSPMV
DSPMV performs the matrixvector 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  AP  AP is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION. 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 DOUBLE PRECISION 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 22October1986. 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 dspmv.f.
subroutine dspr  (  character  UPLO, 
integer  N,  
double precision  ALPHA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision, dimension(*)  AP  
) 
DSPR
DSPR 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 22October1986. 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 dspr.f.
subroutine dspr2  (  character  UPLO, 
integer  N,  
double precision  ALPHA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision, dimension(*)  Y,  
integer  INCY,  
double precision, dimension(*)  AP  
) 
DSPR2
DSPR2 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 22October1986. 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 dspr2.f.
subroutine dsymv  (  character  UPLO, 
integer  N,  
double precision  ALPHA,  
double precision, dimension(lda,*)  A,  
integer  LDA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision  BETA,  
double precision, dimension(*)  Y,  
integer  INCY  
) 
DSYMV
DSYMV performs the matrixvector 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION. 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 DOUBLE PRECISION 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 22October1986. 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 dsymv.f.
subroutine dsyr  (  character  UPLO, 
integer  N,  
double precision  ALPHA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision, dimension(lda,*)  A,  
integer  LDA  
) 
DSYR
DSYR 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 22October1986. 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 dsyr.f.
subroutine dsyr2  (  character  UPLO, 
integer  N,  
double precision  ALPHA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision, dimension(*)  Y,  
integer  INCY,  
double precision, dimension(lda,*)  A,  
integer  LDA  
) 
DSYR2
DSYR2 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 22October1986. 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 dsyr2.f.
subroutine dtbmv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
integer  K,  
double precision, dimension(lda,*)  A,  
integer  LDA,  
double precision, dimension(*)  X,  
integer  INCX  
) 
DTBMV
DTBMV performs one of the matrixvector 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 nonunit, 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 superdiagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of subdiagonals of the matrix A. K must satisfy 0 .le. K. 
[in]  A  A is DOUBLE PRECISION 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 superdiagonal 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 subdiagonal 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 DOUBLE PRECISION 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 22October1986. 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 dtbmv.f.
subroutine dtbsv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
integer  K,  
double precision, dimension(lda,*)  A,  
integer  LDA,  
double precision, dimension(*)  X,  
integer  INCX  
) 
DTBSV
DTBSV 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 nonunit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. No test for singularity or nearsingularity 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 superdiagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of subdiagonals of the matrix A. K must satisfy 0 .le. K. 
[in]  A  A is DOUBLE PRECISION 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 superdiagonal 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 subdiagonal 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 DOUBLE PRECISION array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element righthand 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 22October1986. 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 dtbsv.f.
subroutine dtpmv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
double precision, dimension(*)  AP,  
double precision, dimension(*)  X,  
integer  INCX  
) 
DTPMV
DTPMV performs one of the matrixvector 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 nonunit, 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 22October1986. 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 dtpmv.f.
subroutine dtpsv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
double precision, dimension(*)  AP,  
double precision, dimension(*)  X,  
integer  INCX  
) 
DTPSV
DTPSV 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 nonunit, upper or lower triangular matrix, supplied in packed form. No test for singularity or nearsingularity 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 DOUBLE PRECISION 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 DOUBLE PRECISION array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element righthand 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 22October1986. 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 dtpsv.f.
subroutine dtrmv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
double precision, dimension(lda,*)  A,  
integer  LDA,  
double precision, dimension(*)  X,  
integer  INCX  
) 
DTRMV
DTRMV performs one of the matrixvector 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 nonunit, 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 22October1986. 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 dtrmv.f.