8.6.0.5. BLAS: Double Precision Complex Functions
|
(packages/blas/blas-z.lsh) |
Author(s): Fu Jie
Huang, Yann LeCun
This provides a complete interface to the FORTRAN BLAS library of
low-level linear algebra functions.
8.6.0.5.0. (zaxpy n za zx incx zy incy )
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(packages/blas/blas-z.lsh) |
* =====================================================================
*
* constant times a vector plus a vector.
* jack dongarra, 3/11/78.
* modified 12/3/93, array(1) declarations changed to array(*)
*
* =====================================================================
8.6.0.5.1. (zcopy n zx incx zy incy )
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(packages/blas/blas-z.lsh) |
* =====================================================================
*
* copies a vector, x, to a vector, y.
* jack dongarra, linpack, 4/11/78.
* modified 12/3/93, array(1) declarations changed to array(*)
*
* =====================================================================
8.6.0.5.2. (zdotc n zx incx zy incy )
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(packages/blas/blas-z.lsh) |
* =====================================================================
*
* forms the dot product of a vector.
* jack dongarra, 3/11/78.
* modified 12/3/93, array(1) declarations changed to array(*)
*
* =====================================================================
8.6.0.5.3. (zdotu n zx incx zy incy )
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(packages/blas/blas-z.lsh) |
* =====================================================================
*
* forms the dot product of two vectors.
* jack dongarra, 3/11/78.
* modified 12/3/93, array(1) declarations changed to array(*)
*
* =====================================================================
8.6.0.5.4. (zdscal n da zx incx )
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(packages/blas/blas-z.lsh) |
* =====================================================================
*
* scales a vector by a constant.
* jack dongarra, 3/11/78.
* modified 3/93 to return if incx .le. 0.
* modified 12/3/93, array(1) declarations changed to array(*)
*
* =====================================================================
8.6.0.5.5. (zgbmv trans m n kl ku alpha a lda x incx beta y incy )
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(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZGBMV performs one of the matrix-vector operations
*
* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
*
* y := alpha*conjg( A' )*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.
*
* Parameters
* ==========
*
* TRANS - 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'*x + beta*y.
*
* TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.
*
* Unchanged on exit.
*
* M - INTEGER.
* On entry, M specifies the number of rows of the matrix A.
* M must be at least zero.
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the number of columns of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* KL - INTEGER.
* On entry, KL specifies the number of sub-diagonals of the
* matrix A. KL must satisfy 0 .le. KL.
* Unchanged on exit.
*
* KU - INTEGER.
* On entry, KU specifies the number of super-diagonals of the
* matrix A. KU must satisfy 0 .le. KU.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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
*
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* X - COMPLEX*16 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.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then Y need not be set on input.
* Unchanged on exit.
*
* Y - COMPLEX*16 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.
*
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.6. (zgemm transa transb m n k alpha a lda b ldb beta c ldc )
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(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZGEMM performs one of the matrix-matrix operations
*
* C := alpha*op( A )*op( B ) + beta*C,
*
* where op( X ) is one of
*
* op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ),
*
* alpha and beta are scalars, and A, B and C are matrices, with op( A )
* an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
*
* Parameters
* ==========
*
* TRANSA - 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'.
*
* TRANSA = 'C' or 'c', op( A ) = conjg( A' ).
*
* Unchanged on exit.
*
* TRANSB - 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'.
*
* TRANSB = 'C' or 'c', op( B ) = conjg( B' ).
*
* Unchanged on exit.
*
* M - 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.
* Unchanged on exit.
*
* N - 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.
* Unchanged on exit.
*
* K - 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.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* B - COMPLEX*16 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.
* Unchanged on exit.
*
* LDB - 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 ).
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then C need not be set on input.
* Unchanged on exit.
*
* C - COMPLEX*16 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 ).
*
* LDC - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
* .. External Functions ..
* =====================================================================
8.6.0.5.7. (zgemv trans m n alpha a lda x incx beta y incy )
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(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZGEMV performs one of the matrix-vector operations
*
* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
*
* y := alpha*conjg( A' )*x + beta*y,
*
* where alpha and beta are scalars, x and y are vectors and A is an
* m by n matrix.
*
* Parameters
* ==========
*
* TRANS - 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'*x + beta*y.
*
* TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.
*
* Unchanged on exit.
*
* M - INTEGER.
* On entry, M specifies the number of rows of the matrix A.
* M must be at least zero.
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the number of columns of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 array of DIMENSION ( LDA, n ).
* Before entry, the leading m by n part of the array A must
* contain the matrix of coefficients.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* X - COMPLEX*16 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.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then Y need not be set on input.
* Unchanged on exit.
*
* Y - COMPLEX*16 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.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.8. (zgerc m n alpha x incx y incy a lda )
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(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZGERC performs the rank 1 operation
*
* A := alpha*x*conjg( y' ) + 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.
*
* Parameters
* ==========
*
* M - INTEGER.
* On entry, M specifies the number of rows of the matrix A.
* M must be at least zero.
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the number of columns of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX*16 array of dimension at least
* ( 1 + ( m - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the m
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* Y - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
*
* LDA - 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 ).
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.9. (zgeru m n alpha x incx y incy a lda )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZGERU performs the rank 1 operation
*
* A := alpha*x*y' + 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.
*
* Parameters
* ==========
*
* M - INTEGER.
* On entry, M specifies the number of rows of the matrix A.
* M must be at least zero.
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the number of columns of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX*16 array of dimension at least
* ( 1 + ( m - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the m
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* Y - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
*
* LDA - 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 ).
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.10. (zhbmv uplo n k alpha a lda x incx beta y incy )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHBMV 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 hermitian band matrix, with k super-diagonals.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* K - INTEGER.
* On entry, K specifies the number of super-diagonals of the
* matrix A. K must satisfy 0 .le. K.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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 hermitian 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 hermitian 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 hermitian 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 hermitian 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 the imaginary parts of the diagonal elements need
* not be set and are assumed to be zero.
* Unchanged on exit.
*
* LDA - INTEGER.
* On entry, LDA specifies the first dimension of A as declared
* in the calling (sub) program. LDA must be at least
* ( k + 1 ).
* Unchanged on exit.
*
* X - COMPLEX*16 array of DIMENSION at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the
* vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta.
* Unchanged on exit.
*
* Y - COMPLEX*16 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.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.11. (zhemm side uplo m n alpha a lda b ldb beta c ldc )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHEMM performs one of the matrix-matrix operations
*
* C := alpha*A*B + beta*C,
*
* or
*
* C := alpha*B*A + beta*C,
*
* where alpha and beta are scalars, A is an hermitian matrix and B and
* C are m by n matrices.
*
* Parameters
* ==========
*
* SIDE - CHARACTER*1.
* On entry, SIDE specifies whether the hermitian 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,
*
* Unchanged on exit.
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the upper or lower
* triangular part of the hermitian matrix A is to be
* referenced as follows:
*
* UPLO = 'U' or 'u' Only the upper triangular part of the
* hermitian matrix is to be referenced.
*
* UPLO = 'L' or 'l' Only the lower triangular part of the
* hermitian matrix is to be referenced.
*
* Unchanged on exit.
*
* M - INTEGER.
* On entry, M specifies the number of rows of the matrix C.
* M must be at least zero.
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the number of columns of the matrix C.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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 hermitian 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 hermitian 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 hermitian
* 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 hermitian 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 hermitian 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 hermitian
* matrix and the strictly upper triangular part of A is not
* referenced.
* Note that the imaginary parts of the diagonal elements need
* not be set, they are assumed to be zero.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* B - COMPLEX*16 array of DIMENSION ( LDB, n ).
* Before entry, the leading m by n part of the array B must
* contain the matrix B.
* Unchanged on exit.
*
* LDB - 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 ).
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then C need not be set on input.
* Unchanged on exit.
*
* C - COMPLEX*16 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.
*
* LDC - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
* .. External Functions ..
* =====================================================================
8.6.0.5.12. (zhemv uplo n alpha a lda x incx beta y incy )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHEMV 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 hermitian matrix.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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 hermitian 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 hermitian matrix and the strictly
* upper triangular part of A is not referenced.
* Note that the imaginary parts of the diagonal elements need
* not be set and are assumed to be zero.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* X - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then Y need not be set on input.
* Unchanged on exit.
*
* Y - COMPLEX*16 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.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.13. (zher2k uplo trans n k alpha a lda b ldb beta c ldc )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHER2K performs one of the hermitian rank 2k operations
*
* C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
*
* or
*
* C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,
*
* where alpha and beta are scalars with beta real, C is an n by n
* hermitian matrix and A and B are n by k matrices in the first case
* and k by n matrices in the second case.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) +
* conjg( alpha )*B*conjg( A' ) +
* beta*C.
*
* TRANS = 'C' or 'c' C := alpha*conjg( A' )*B +
* conjg( alpha )*conjg( B' )*A +
* beta*C.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix C. N must be
* at least zero.
* Unchanged on exit.
*
* K - 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 = 'C' or 'c', K specifies the number of rows of the
* matrices A and B. K must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* B - COMPLEX*16 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.
* Unchanged on exit.
*
* LDB - 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 ).
* Unchanged on exit.
*
* BETA - DOUBLE PRECISION .
* On entry, BETA specifies the scalar beta.
* Unchanged on exit.
*
* C - COMPLEX*16 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 hermitian 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 hermitian 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.
* Note that the imaginary parts of the diagonal elements need
* not be set, they are assumed to be zero, and on exit they
* are set to zero.
*
* LDC - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
* -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
* Ed Anderson, Cray Research Inc.
*
*
* .. External Functions ..
* =====================================================================
8.6.0.5.14. (zher2 uplo n alpha x incx y incy a lda )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHER2 performs the hermitian rank 2 operation
*
* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
*
* where alpha is a scalar, x and y are n element vectors and A is an n
* by n hermitian matrix.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* Y - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
* A - COMPLEX*16 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 hermitian 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 hermitian 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.
* Note that the imaginary parts of the diagonal elements need
* not be set, they are assumed to be zero, and on exit they
* are set to zero.
*
* LDA - 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 ).
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.15. (zherk uplo trans n k alpha a lda beta c ldc )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHERK performs one of the hermitian rank k operations
*
* C := alpha*A*conjg( A' ) + beta*C,
*
* or
*
* C := alpha*conjg( A' )*A + beta*C,
*
* where alpha and beta are real scalars, C is an n by n hermitian
* matrix and A is an n by k matrix in the first case and a k by n
* matrix in the second case.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C.
*
* TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix C. N must be
* at least zero.
* Unchanged on exit.
*
* K - INTEGER.
* On entry with TRANS = 'N' or 'n', K specifies the number
* of columns of the matrix A, and on entry with
* TRANS = 'C' or 'c', K specifies the number of rows of the
* matrix A. K must be at least zero.
* Unchanged on exit.
*
* ALPHA - DOUBLE PRECISION .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* BETA - DOUBLE PRECISION.
* On entry, BETA specifies the scalar beta.
* Unchanged on exit.
*
* C - COMPLEX*16 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 hermitian 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 hermitian 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.
* Note that the imaginary parts of the diagonal elements need
* not be set, they are assumed to be zero, and on exit they
* are set to zero.
*
* LDC - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
* -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
* Ed Anderson, Cray Research Inc.
*
*
* .. External Functions ..
* =====================================================================
8.6.0.5.16. (zher uplo n alpha x incx a lda )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHER performs the hermitian rank 1 operation
*
* A := alpha*x*conjg( x' ) + A,
*
* where alpha is a real scalar, x is an n element vector and A is an
* n by n hermitian matrix.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - DOUBLE PRECISION.
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* A - COMPLEX*16 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 hermitian 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 hermitian 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.
* Note that the imaginary parts of the diagonal elements need
* not be set, they are assumed to be zero, and on exit they
* are set to zero.
*
* LDA - 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 ).
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.17. (zhpmv uplo n alpha ap x incx beta y incy )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHPMV 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 hermitian matrix, supplied in packed form.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* AP - COMPLEX*16 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 hermitian 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 hermitian 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 the imaginary parts of the diagonal elements need
* not be set and are assumed to be zero.
* Unchanged on exit.
*
* X - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then Y need not be set on input.
* Unchanged on exit.
*
* Y - COMPLEX*16 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.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.18. (zhpr2 uplo n alpha x incx y incy ap )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHPR2 performs the hermitian rank 2 operation
*
* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
*
* where alpha is a scalar, x and y are n element vectors and A is an
* n by n hermitian matrix, supplied in packed form.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* Y - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
* AP - COMPLEX*16 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 hermitian 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 hermitian 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.
* Note that the imaginary parts of the diagonal elements need
* not be set, they are assumed to be zero, and on exit they
* are set to 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.19. (zhpr uplo n alpha x incx ap )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZHPR performs the hermitian rank 1 operation
*
* A := alpha*x*conjg( x' ) + A,
*
* where alpha is a real scalar, x is an n element vector and A is an
* n by n hermitian matrix, supplied in packed form.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - DOUBLE PRECISION.
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* AP - COMPLEX*16 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 hermitian 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 hermitian 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.
* Note that the imaginary parts of the diagonal elements need
* not be set, they are assumed to be zero, and on exit they
* are set to 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.20. (zrotg ca cb c s )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* =====================================================================
8.6.0.5.21. (zscal n za zx incx )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
*
* scales a vector by a constant.
* jack dongarra, 3/11/78.
* modified 3/93 to return if incx .le. 0.
* modified 12/3/93, array(1) declarations changed to array(*)
*
* =====================================================================
8.6.0.5.22. (zswap n zx incx zy incy )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
*
* interchanges two vectors.
* jack dongarra, 3/11/78.
* modified 12/3/93, array(1) declarations changed to array(*)
*
* =====================================================================
8.6.0.5.23. (zsymm side uplo m n alpha a lda b ldb beta c ldc )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZSYMM performs one of the matrix-matrix operations
*
* C := alpha*A*B + beta*C,
*
* or
*
* C := alpha*B*A + beta*C,
*
* where alpha and beta are scalars, A is a symmetric matrix and B and
* C are m by n matrices.
*
* Parameters
* ==========
*
* SIDE - 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,
*
* Unchanged on exit.
*
* UPLO - 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.
*
* Unchanged on exit.
*
* M - INTEGER.
* On entry, M specifies the number of rows of the matrix C.
* M must be at least zero.
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the number of columns of the matrix C.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* B - COMPLEX*16 array of DIMENSION ( LDB, n ).
* Before entry, the leading m by n part of the array B must
* contain the matrix B.
* Unchanged on exit.
*
* LDB - 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 ).
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then C need not be set on input.
* Unchanged on exit.
*
* C - COMPLEX*16 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.
*
* LDC - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
* .. External Functions ..
* =====================================================================
8.6.0.5.24. (zsyr2k uplo trans n k alpha a lda b ldb beta c ldc )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZSYR2K performs one of the symmetric rank 2k operations
*
* C := alpha*A*B' + alpha*B*A' + beta*C,
*
* or
*
* C := alpha*A'*B + alpha*B'*A + beta*C,
*
* where alpha and beta are scalars, C is an n by n symmetric matrix
* and A and B are n by k matrices in the first case and k by n
* matrices in the second case.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
* beta*C.
*
* TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
* beta*C.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix C. N must be
* at least zero.
* Unchanged on exit.
*
* K - 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', K specifies the number of rows of the
* matrices A and B. K must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* B - COMPLEX*16 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.
* Unchanged on exit.
*
* LDB - 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 ).
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta.
* Unchanged on exit.
*
* C - COMPLEX*16 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.
*
* LDC - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
* .. External Functions ..
* =====================================================================
8.6.0.5.25. (zsyrk uplo trans n k alpha a lda beta c ldc )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZSYRK performs one of the symmetric rank k operations
*
* C := alpha*A*A' + beta*C,
*
* or
*
* C := alpha*A'*A + beta*C,
*
* where alpha and beta are scalars, C is an n by n symmetric matrix
* and A is an n by k matrix in the first case and a k by n matrix
* in the second case.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' C := alpha*A*A' + beta*C.
*
* TRANS = 'T' or 't' C := alpha*A'*A + beta*C.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix C. N must be
* at least zero.
* Unchanged on exit.
*
* K - 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', K specifies the number of rows of the
* matrix A. K must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta.
* Unchanged on exit.
*
* C - COMPLEX*16 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.
*
* LDC - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
* .. External Functions ..
* =====================================================================
8.6.0.5.26. (ztbmv uplo trans diag n k a lda x incx )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZTBMV performs one of the matrix-vector operations
*
* x := A*x, or x := A'*x, or x := conjg( A' )*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.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - 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'*x.
*
* TRANS = 'C' or 'c' x := conjg( A' )*x.
*
* Unchanged on exit.
*
* DIAG - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* K - 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.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - INTEGER.
* On entry, LDA specifies the first dimension of A as declared
* in the calling (sub) program. LDA must be at least
* ( k + 1 ).
* Unchanged on exit.
*
* X - COMPLEX*16 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.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.27. (ztbsv uplo trans diag n k a lda x incx )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZTBSV solves one of the systems of equations
*
* A*x = b, or A'*x = b, or conjg( A' )*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.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - 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'*x = b.
*
* TRANS = 'C' or 'c' conjg( A' )*x = b.
*
* Unchanged on exit.
*
* DIAG - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* K - 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.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - INTEGER.
* On entry, LDA specifies the first dimension of A as declared
* in the calling (sub) program. LDA must be at least
* ( k + 1 ).
* Unchanged on exit.
*
* X - COMPLEX*16 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.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.28. (ztpmv uplo trans diag n ap x incx )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZTPMV performs one of the matrix-vector operations
*
* x := A*x, or x := A'*x, or x := conjg( A' )*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.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - 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'*x.
*
* TRANS = 'C' or 'c' x := conjg( A' )*x.
*
* Unchanged on exit.
*
* DIAG - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* AP - COMPLEX*16 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.
* Unchanged on exit.
*
* X - COMPLEX*16 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.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.29. (ztpsv uplo trans diag n ap x incx )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZTPSV solves one of the systems of equations
*
* A*x = b, or A'*x = b, or conjg( A' )*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.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - 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'*x = b.
*
* TRANS = 'C' or 'c' conjg( A' )*x = b.
*
* Unchanged on exit.
*
* DIAG - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* AP - COMPLEX*16 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.
* Unchanged on exit.
*
* X - COMPLEX*16 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.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.30. (ztrmm side uplo transa diag m n alpha a lda b ldb )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZTRMM performs one of the matrix-matrix operations
*
* B := alpha*op( A )*B, or B := alpha*B*op( A )
*
* where alpha is a scalar, B is an m by n matrix, A is a unit, or
* non-unit, upper or lower triangular matrix and op( A ) is one of
*
* op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ).
*
* Parameters
* ==========
*
* SIDE - 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 ).
*
* Unchanged on exit.
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANSA - 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'.
*
* TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
*
* Unchanged on exit.
*
* DIAG - 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.
*
* Unchanged on exit.
*
* M - INTEGER.
* On entry, M specifies the number of rows of B. M must be at
* least zero.
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the number of columns of B. N must be
* at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha. When alpha is
* zero then A is not referenced and B need not be set before
* entry.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* B - COMPLEX*16 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.
*
* LDB - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
* .. External Functions ..
* =====================================================================
8.6.0.5.31. (ztrmv uplo trans diag n a lda x incx )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZTRMV performs one of the matrix-vector operations
*
* x := A*x, or x := A'*x, or x := conjg( A' )*x,
*
* where x is an n element vector and A is an n by n unit, or non-unit,
* upper or lower triangular matrix.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - 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'*x.
*
* TRANS = 'C' or 'c' x := conjg( A' )*x.
*
* Unchanged on exit.
*
* DIAG - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* X - COMPLEX*16 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.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================
8.6.0.5.32. (ztrsm side uplo transa diag m n alpha a lda b ldb )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZTRSM solves one of the matrix equations
*
* op( A )*X = alpha*B, or X*op( A ) = alpha*B,
*
* where alpha is a scalar, X and B are m by n matrices, A is a unit, or
* non-unit, upper or lower triangular matrix and op( A ) is one of
*
* op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ).
*
* The matrix X is overwritten on B.
*
* Parameters
* ==========
*
* SIDE - 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.
*
* Unchanged on exit.
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANSA - 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'.
*
* TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
*
* Unchanged on exit.
*
* DIAG - 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.
*
* Unchanged on exit.
*
* M - INTEGER.
* On entry, M specifies the number of rows of B. M must be at
* least zero.
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the number of columns of B. N must be
* at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha. When alpha is
* zero then A is not referenced and B need not be set before
* entry.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* B - COMPLEX*16 array of DIMENSION ( LDB, n ).
* Before entry, the leading m by n part of the array B must
* contain the right-hand side matrix B, and on exit is
* overwritten by the solution matrix X.
*
* LDB - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
* .. External Functions ..
* =====================================================================
8.6.0.5.33. (ztrsv uplo trans diag n a lda x incx )
|
(packages/blas/blas-z.lsh) |
* =====================================================================
* Purpose
* =======
*
* ZTRSV solves one of the systems of equations
*
* A*x = b, or A'*x = b, or conjg( A' )*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.
*
* Parameters
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANS - 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'*x = b.
*
* TRANS = 'C' or 'c' conjg( A' )*x = b.
*
* Unchanged on exit.
*
* DIAG - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* A - COMPLEX*16 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* X - COMPLEX*16 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.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
*
* 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.
*
*
* .. Parameters ..
* =====================================================================