;;; -*- Mode: lisp; Syntax: ansi-common-lisp; Package: :blas; Base: 10 -*- ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; ;;; Copyright (c) 2000 The Regents of the University of California. ;;; All rights reserved. ;;; ;;; Permission is hereby granted, without written agreement and without ;;; license or royalty fees, to use, copy, modify, and distribute this ;;; software and its documentation for any purpose, provided that the ;;; above copyright notice and the following two paragraphs appear in all ;;; copies of this software. ;;; ;;; IN NO EVENT SHALL THE UNIVERSITY OF CALIFORNIA BE LIABLE TO ANY PARTY ;;; FOR DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ;;; ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN IF ;;; THE UNIVERSITY OF CALIFORNIA HAS BEEN ADVISED OF THE POSSIBILITY OF ;;; SUCH DAMAGE. ;;; ;;; THE UNIVERSITY OF CALIFORNIA SPECIFICALLY DISCLAIMS ANY WARRANTIES, ;;; INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF ;;; MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE ;;; PROVIDED HEREUNDER IS ON AN "AS IS" BASIS, AND THE UNIVERSITY OF ;;; CALIFORNIA HAS NO OBLIGATION TO PROVIDE MAINTENANCE, SUPPORT, UPDATES, ;;; ENHANCEMENTS, OR MODIFICATIONS. ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; ;;; Originally written by Tunc Simsek, Univ. of California, Berkeley ;;; 1999, simsek@eecs.berkeley.edu ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; ;;; $Id: blas.lisp,v 1.6 2004/05/24 16:34:22 rtoy Exp $ ;;; ;;; $Log: blas.lisp,v $ ;;; Revision 1.6 2004/05/24 16:34:22 rtoy ;;; More SBCL support from Robert Sedgewick. The previous SBCL support ;;; was incomplete. ;;; ;;; Revision 1.5 2001/02/21 19:31:13 simsek ;;; o Fixed minor typos and doc strings ;;; ;;; Revision 1.4 2000/07/11 18:02:03 simsek ;;; o Added credits ;;; ;;; Revision 1.3 2000/07/11 02:11:56 simsek ;;; o Added support for Allegro CL ;;; ;;; Revision 1.2 2000/06/19 22:21:45 rtoy ;;; Define packages elsewhere. ;;; ;;; Revision 1.1 2000/04/14 00:12:48 simsek ;;; Initial revision. ;;; ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; (in-package :f77) (def-fortran-routine daxpy :void " Syntax ====== (DAXPY n a x incx y incy) Purpose ======= Y <- A*X + Y Arguments ========= N (input) FIXNUM Number of elements of X,Y to be operated on. A (input) DOUBLE-FLOAT X (input) (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(INCX), ... , X((N-1)*INCX) Y (input/output) (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCY (input) FIXNUM Determines the position of the elements in Y. Usually INCY is 1. If INCY is bigger than 1 then the elements considered in the operations are: Y(0),Y(INCY), ... , Y((N-1)*INCY) " (n :integer :input) (da :double-float :input) (dx (* :double-float)) (incx :integer :input) (dy (* :double-float) :output) (incy :integer :input) ) (def-fortran-routine dcopy :void " Syntax ====== (DCOPY n x incx y incy) Purpose ======= Y <- X Arguments ========= N (input) FIXNUM Number of elements of X,Y to be operated on. X (input) (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(INCX), ... , X((N-1)*INCX) Y (input/output) (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCY (input) FIXNUM Determines the position of the elements in Y. Usually INCY is 1. If INCY is bigger than 1 then the elements considered in the operations are: Y(0),Y(INCY), ... , Y((N-1)*INCY) " (n :integer :input) (dx (* :double-float)) (incx :integer :input) (dy (* :double-float) :output) (incy :integer :input) ) (def-fortran-routine drot :void (n :integer :input) (dx (* :double-float) :output) (incx :integer :input) (dy (* :double-float) :output) (incy :integer :input) (c :double-float :output) (s :double-float :output) ) #| (def-fortran-routine drotg :void (da :double-float :output) (db :double-float :output) (c :double-float :output) (s :double-float :output) ) |# (def-fortran-routine dscal :void " Syntax ====== (DSCAL n a x incx) Purpose ======= X <- A*X Arguments ========= N (input) FIXNUM Number of elements of X to be operated on. X (input) (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(INCX), ... , X((N-1)*INCX) " (n :integer :input) (da :double-float :input) (dx (* :double-float) :output) (incx :integer :input) ) (def-fortran-routine dswap :void " Syntax ====== (DSWAP n x incx y incy) Purpose ======= Y <-> X Arguments ========= N (input) FIXNUM Number of elements of X,Y to be operated on. X (input) (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(INCX), ... , X((N-1)*INCX) Y (input/output) (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCY (input) FIXNUM Determines the position of the elements in Y. Usually INCY is 1. If INCY is bigger than 1 then the elements considered in the operations are: Y(0),Y(INCY), ... , Y((N-1)*INCY) " (n :integer :input) (dx (* :double-float) :output) (incx :integer :input) (dy (* :double-float)) (incy :integer :input) ) (def-fortran-routine zaxpy :void " Syntax ====== (ZAXPY n a x incx y incy) Purpose ======= Y <- A*X + Y Arguments ========= N (input) FIXNUM Number of elements of X,Y to be operated on. A (input) (COMPLEX DOUBLE-FLOAT) X (input) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(2*INCX), ... , X(2*(N-1)*INCX) Y (input/output) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCY (input) FIXNUM Determines the position of the elements in Y. Usually INCY is 1. If INCY is bigger than 1 then the elements considered in the operations are: Y(0),Y(2*INCY), ... , Y(2*(N-1)*INCY) " (n :integer :input) (za :complex-double-float) (zx (* :complex-double-float)) (incx :integer :input) (zy (* :complex-double-float) :output) (incy :integer :input) ) (def-fortran-routine zcopy :void " Syntax ====== (ZCOPY n x incx y incy) Purpose ======= Y <- X Arguments ========= N (input) FIXNUM Number of elements of X,Y to be operated on. A (input) (COMPLEX DOUBLE-FLOAT) X (input) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(2*INCX), ... , X(2*(N-1)*INCX) Y (input/output) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCY (input) FIXNUM Determines the position of the elements in Y. Usually INCY is 1. If INCY is bigger than 1 then the elements considered in the operations are: Y(0),Y(2*INCY), ... , Y(2*(N-1)*INCY) " (n :integer :input) (zx (* :complex-double-float)) (incx :integer :input) (zy (* :complex-double-float) :output) (incy :integer :input) ) (def-fortran-routine zdscal :void " Syntax ====== (ZDSCAL n a x incx) Purpose ======= X <- A*X Arguments ========= N (input) FIXNUM Number of elements of X to be operated on. A (input) DOUBLE-FLOAT X (input) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(2*INCX), ... , X(2*(N-1)*INCX) " (n :integer :input) (da :double-float :input) (zx (* :complex-double-float) :output) (incx :integer :input) ) #| (def-fortran-routine zrotg :void (ca (* :complex-double-float) :output) (cb (* :complex-double-float) :output) (c :double-float :output) (s (* :complex-double-float) :output) ) |# (def-fortran-routine zscal :void " Syntax ====== (ZSCAL n a x incx) Purpose ======= X <- A*X Arguments ========= N (input) FIXNUM Number of elements of X to be operated on. A (input) (COMPLEX DOUBLE-FLOAT) X (input) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(2*INCX), ... , X(2*(N-1)*INCX) " (n :integer :input) (za :complex-double-float) (zx (* :complex-double-float) :output) (incx :integer :input) ) (def-fortran-routine zswap :void " Syntax ====== (ZSWAP n x incx y incy) Purpose ======= Y <-> X Arguments ========= N (input) FIXNUM Number of elements of X,Y to be operated on. A (input) (COMPLEX DOUBLE-FLOAT) X (input) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(2*INCX), ... , X(2*(N-1)*INCX) Y (input/output) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCY (input) FIXNUM Determines the position of the elements in Y. Usually INCY is 1. If INCY is bigger than 1 then the elements considered in the operations are: Y(0),Y(2*INCY), ... , Y(2*(N-1)*INCY) " (n :integer :input) (zx (* :complex-double-float) :output) (incx :integer :input) (zy (* :complex-double-float)) (incy :integer :input) ) (def-fortran-routine zdotu :complex-double-float " Syntax ====== (ZDOTU n x incx y incy) Purpose ======= ZDOTU <- X^T Y Complex precision inner product of X,Y. Arguments ========= N (input) FIXNUM Number of elements of X,Y to be operated on. X (input) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(2*INCX), ... , X(2*(N-1)*INCX) Y (input) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCY (input) FIXNUM Determines the position of the elements in Y. Usually INCY is 1. If INCY is bigger than 1 then the elements considered in the operations are: Y(0),Y(2*INCY), ... , Y(2*(N-1)*INCY) " (n :integer :input) (zx (* :complex-double-float) :input) (incx :integer :input) (zy (* :complex-double-float) :input) (incy :integer :input) ) (def-fortran-routine zdotc :complex-double-float " Syntax ====== (ZDOTC n x incx y incy) Purpose ======= ZDOTC <- X^H Y Complex precision inner product of X conjugate and Y. Arguments ========= N (input) FIXNUM Number of elements of X,Y to be operated on. X (input) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(2*INCX), ... , X(2*(N-1)*INCX) Y (input) (SIMPLE-ARRAY (COMPLEX DOUBLE-FLOAT) (*)) represented as (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCY (input) FIXNUM Determines the position of the elements in Y. Usually INCY is 1. If INCY is bigger than 1 then the elements considered in the operations are: Y(0),Y(2*INCY), ... , Y(2*(N-1)*INCY) " (n :integer :input) (zx (* :complex-double-float) :input) (incx :integer :input) (zy (* :complex-double-float) :input) (incy :integer :input) ) (def-fortran-routine idamax :integer " " (n :integer :input) (dx (* :double-float) :input) (incx :integer :input) ) (def-fortran-routine dasum :double-float " " (n :integer :input) (dx (* :double-float) :input) (incx :integer :input) ) (def-fortran-routine ddot :double-float " Syntax ====== (DDOT n x incx y incy) Purpose ======= DDOT <- X^T Y Double precision inner product of X,Y. Arguments ========= N (input) FIXNUM Number of elements of X,Y to be operated on. X (input) (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCX (input) FIXNUM Determines the position of the elements in X. Usually INCX is 1. If INCX is bigger than 1 then the elements considered in the operations are: X(0),X(2*INCX), ... , X(2*(N-1)*INCX) Y (input) (SIMPLE-ARRAY DOUBLE-FLOAT (*)) INCY (input) FIXNUM Determines the position of the elements in Y. Usually INCY is 1. If INCY is bigger than 1 then the elements considered in the operations are: Y(0),Y(2*INCY), ... , Y(2*(N-1)*INCY) " (n :integer :input) (dx (* :double-float) :input) (incx :integer :input) (dy (* :double-float) :input) (incy :integer :input) ) (def-fortran-routine dnrm2 :double-float " " (n :integer :input) (x (* :double-float) :input) (incx :integer :input) ) (def-fortran-routine dgemv :void " Purpose ======= DGEMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*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*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 - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - 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. 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 - 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. 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 - DOUBLE PRECISION. 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 - 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 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. " (trans :string :input) (m :integer ) (n :integer ) (alpha :double-float ) (a (* :double-float) ) (lda :integer ) (x (* :double-float) ) (incx :integer ) (beta :double-float ) (y (* :double-float) :output) (incy :integer ) ) (def-fortran-routine dsymv :void " Purpose ======= DSYMV performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix. 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. A - 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. 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 - 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. 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 - DOUBLE PRECISION. 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 - 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. 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. " (uplo :string :input) (n :integer ) (alpha :double-float ) (a (* :double-float) ) (lda :integer ) (x (* :double-float) ) (incx :integer ) (beta :double-float ) (y (* :double-float) :output) (incy :integer ) ) (def-fortran-routine dtrmv :void " Purpose ======= DTRMV performs one of the matrix-vector operations x := A*x, or x := 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 := 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 - 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. 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 - 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. 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. " (uplo :string :input) (trans :string :input) (diag :string :input) (n :integer ) (a (* :double-float) ) (lda :integer ) (x (* :double-float) :output) (incx :integer ) ) (def-fortran-routine dtrsv :void " Purpose ======= DTRSV solves one of the systems of equations A*x = b, or 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' 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 - 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. 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 - DOUBLE PRECISION 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. " (uplo :string :input) (trans :string :input) (diag :string :input) (n :integer ) (a (* :double-float) ) (lda :integer ) (x (* :double-float) :output) (incx :integer ) ) (def-fortran-routine dger :void " Purpose ======= DGER 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 - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. X - 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. 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 - 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. 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 - 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. 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. " (m :integer ) (n :integer ) (alpha :double-float ) (x (* :double-float) ) (incx :integer ) (y (* :double-float) ) (incy :integer ) (a (* :double-float) :output) (lda :integer ) ) (def-fortran-routine dsyr :void " Purpose ======= DSYR performs the symmetric rank 1 operation A := alpha*x*x' + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric 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 - 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. 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 - 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. 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. " (uplo :string :input) (n :integer ) (alpha :double-float ) (x (* :double-float) ) (incx :integer ) (a (* :double-float) :output) (lda :integer ) ) (def-fortran-routine dsyr2 :void " Purpose ======= DSYR2 performs the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric 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 - 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. 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 - 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. 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 - 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. 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. " (uplo :string :input) (n :integer ) (alpha :double-float ) (x (* :double-float) ) (incx :integer ) (y (* :double-float) ) (incy :integer ) (a (* :double-float) :output) (lda :integer ) ) (def-fortran-routine dgemm :void " Purpose ======= DGEMM performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = X', 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 ) = 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 ) = 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 - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION. 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 - DOUBLE PRECISION 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. " (transa :string :input) (transb :string :input) (m :integer ) (n :integer ) (k :integer ) (alpha :double-float ) (a (* :double-float) ) (lda :integer ) (b (* :double-float) ) (ldb :integer ) (beta :double-float ) (c (* :double-float) :output) (ldc :integer ) ) (def-fortran-routine dsyrk :void " Purpose ======= DSYRK 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. TRANS = 'C' or 'c' 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' or '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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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. " (uplo :string :input) (trans :string :input) (n :integer ) (k :integer ) (alpha :double-float ) (a (* :double-float) ) (lda :integer ) (beta :double-float ) (c (* :double-float) :output) (ldc :integer ) ) (def-fortran-routine dsyr2k :void " Purpose ======= DSYR2K 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. TRANS = 'C' or 'c' 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' or '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 - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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. " (uplo :string :input) (trans :string :input) (n :integer ) (k :integer ) (alpha :double-float ) (a (* :double-float) ) (lda :integer ) (b (* :double-float) ) (ldb :integer ) (beta :double-float ) (c (* :double-float) :output) (ldc :integer ) ) (def-fortran-routine dtrmm :void " Purpose ======= DTRMM 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'. 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 ) = 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 - DOUBLE PRECISION. 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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. " (side :string :input) (uplo :string :input) (transa :string :input) (diag :string :input) (m :integer ) (n :integer ) (alpha :double-float ) (a (* :double-float) ) (lda :integer ) (b (* :double-float) :output) (ldb :integer ) ) (def-fortran-routine dtrsm :void " Purpose ======= DTRSM 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'. 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 ) = 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 - DOUBLE PRECISION. 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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. " (side :string :input) (uplo :string :input) (transa :string :input) (diag :string :input) (m :integer ) (n :integer ) (alpha :double-float ) (a (* :double-float) ) (lda :integer ) (b (* :double-float) :output) (ldb :integer ) ) (def-fortran-routine dcabs1 :double-float " " (z :complex-double-float :input) ) (def-fortran-routine dzasum :double-float " " (n :integer :input) (zx (* :complex-double-float) :input) (incx :integer :input) ) (def-fortran-routine dznrm2 :double-float " " (n :integer :input) (x (* :complex-double-float) :input) (incx :integer :input) ) (def-fortran-routine izamax :integer " " (n :integer :input) (zx (* :complex-double-float) :input) (incx :integer :input) ) (def-fortran-routine zgemv :void " 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. " (trans :string :input) (m :integer ) (n :integer ) (alpha :complex-double-float ) (a (* :complex-double-float) ) (lda :integer ) (x (* :complex-double-float) ) (incx :integer ) (beta :complex-double-float ) (y (* :complex-double-float) :output) (incy :integer ) ) (def-fortran-routine zhemv :void " 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. " (uplo :string :input) (n :integer ) (alpha :complex-double-float ) (a (* :complex-double-float) ) (lda :integer ) (x (* :complex-double-float) ) (incx :integer ) (beta :complex-double-float ) (y (* :complex-double-float) :output) (incy :integer ) ) (def-fortran-routine ztrmv :void " 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. " (uplo :string :input) (trans :string :input) (diag :string :input) (n :integer ) (a (* :complex-double-float) ) (lda :integer ) (x (* :complex-double-float) :output) (incx :integer ) ) (def-fortran-routine ztrsv :void " 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. " (uplo :string :input) (trans :string :input) (diag :string :input) (n :integer ) (a (* :complex-double-float) ) (lda :integer ) (x (* :complex-double-float) :output) (incx :integer ) ) (def-fortran-routine zgerc :void " 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. " (m :integer ) (n :integer ) (alpha :complex-double-float ) (x (* :complex-double-float) ) (incx :integer ) (y (* :complex-double-float) ) (incy :integer ) (a (* :complex-double-float) :output) (lda :integer ) ) (def-fortran-routine zgeru :void " 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. " (m :integer ) (n :integer ) (alpha :complex-double-float ) (x (* :complex-double-float) ) (incx :integer ) (y (* :complex-double-float) ) (incy :integer ) (a (* :complex-double-float) :output) (lda :integer ) ) (def-fortran-routine zher2 :void " 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. " (uplo :string :input) (n :integer ) (alpha :complex-double-float ) (x (* :complex-double-float) ) (incx :integer ) (y (* :complex-double-float) ) (incy :integer ) (a (* :complex-double-float) :output) (lda :integer ) ) (def-fortran-routine zgemm :void " 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. " (transa :string :input) (transb :string :input) (m :integer ) (n :integer ) (k :integer ) (alpha :complex-double-float ) (a (* :complex-double-float) ) (lda :integer ) (b (* :complex-double-float) ) (ldb :integer ) (beta :complex-double-float ) (c (* :complex-double-float) :output) (ldc :integer ) ) (def-fortran-routine ztrmm :void " 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. " (side :string :input) (uplo :string :input) (transa :string :input) (diag :string :input) (m :integer ) (n :integer ) (alpha :complex-double-float ) (a (* :complex-double-float) ) (lda :integer ) (b (* :complex-double-float) :output) (ldb :integer ) ) (def-fortran-routine ztrsm :void " 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. " (side :string :input) (uplo :string :input) (transa :string :input) (diag :string :input) (m :integer ) (n :integer ) (alpha :complex-double-float ) (a (* :complex-double-float) ) (lda :integer ) (b (* :complex-double-float) :output) (ldb :integer ) ) (def-fortran-routine zherk :void " 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. " (uplo :string :input) (trans :string :input) (n :integer ) (k :integer ) (alpha :double-float ) (a (* :complex-double-float) ) (lda :integer ) (beta :double-float ) (c (* :complex-double-float) :output) (ldc :integer ) ) (def-fortran-routine zher2k :void " 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. " (uplo :string :input) (trans :string :input) (n :integer ) (k :integer ) (alpha :complex-double-float ) (a (* :complex-double-float) ) (lda :integer ) (b (* :complex-double-float) ) (ldb :integer ) (beta :double-float ) (c (* :complex-double-float) :output) (ldc :integer ) )