blas_lite.c
/*
NOTE: This is generated code. Look in README.python for information on
remaking this file.
*/
#include "sphinxbase/f2c.h"
#ifdef HAVE_CONFIG
#include "config.h"
#else
extern doublereal slamch_(char *);
#define EPSILON slamch_("Epsilon")
#define SAFEMINIMUM slamch_("Safe minimum")
#define PRECISION slamch_("Precision")
#define BASE slamch_("Base")
#endif
extern doublereal slapy2_(real *, real *);
/* Table of constant values */
static integer c__1 = 1;
logical lsame_(char *ca, char *cb)
{
/* System generated locals */
logical ret_val;
/* Local variables */
static integer inta, intb, zcode;
/*
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
LSAME returns .TRUE. if CA is the same letter as CB regardless of
case.
Arguments
=========
CA (input) CHARACTER*1
CB (input) CHARACTER*1
CA and CB specify the single characters to be compared.
=====================================================================
Test if the characters are equal
*/
ret_val = *(unsigned char *)ca == *(unsigned char *)cb;
if (ret_val) {
return ret_val;
}
/* Now test for equivalence if both characters are alphabetic. */
zcode = 'Z';
/*
Use 'Z' rather than 'A' so that ASCII can be detected on Prime
machines, on which ICHAR returns a value with bit 8 set.
ICHAR('A') on Prime machines returns 193 which is the same as
ICHAR('A') on an EBCDIC machine.
*/
inta = *(unsigned char *)ca;
intb = *(unsigned char *)cb;
if (zcode == 90 || zcode == 122) {
/*
ASCII is assumed - ZCODE is the ASCII code of either lower or
upper case 'Z'.
*/
if (inta >= 97 && inta <= 122) {
inta += -32;
}
if (intb >= 97 && intb <= 122) {
intb += -32;
}
} else if (zcode == 233 || zcode == 169) {
/*
EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or
upper case 'Z'.
*/
if (inta >= 129 && inta <= 137 || inta >= 145 && inta <= 153 || inta
>= 162 && inta <= 169) {
inta += 64;
}
if (intb >= 129 && intb <= 137 || intb >= 145 && intb <= 153 || intb
>= 162 && intb <= 169) {
intb += 64;
}
} else if (zcode == 218 || zcode == 250) {
/*
ASCII is assumed, on Prime machines - ZCODE is the ASCII code
plus 128 of either lower or upper case 'Z'.
*/
if (inta >= 225 && inta <= 250) {
inta += -32;
}
if (intb >= 225 && intb <= 250) {
intb += -32;
}
}
ret_val = inta == intb;
/*
RETURN
End of LSAME
*/
return ret_val;
} /* lsame_ */
doublereal sdot_(integer *n, real *sx, integer *incx, real *sy, integer *incy)
{
/* System generated locals */
integer i__1;
real ret_val;
/* Local variables */
static integer i__, m, ix, iy, mp1;
static real stemp;
/*
forms the dot product of two vectors.
uses unrolled loops for increments equal to one.
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
*/
/* Parameter adjustments */
--sy;
--sx;
/* Function Body */
stemp = 0.f;
ret_val = 0.f;
if (*n <= 0) {
return ret_val;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp += sx[ix] * sy[iy];
ix += *incx;
iy += *incy;
/* L10: */
}
ret_val = stemp;
return ret_val;
/*
code for both increments equal to 1
clean-up loop
*/
L20:
m = *n % 5;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp += sx[i__] * sy[i__];
/* L30: */
}
if (*n < 5) {
goto L60;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 5) {
stemp = stemp + sx[i__] * sy[i__] + sx[i__ + 1] * sy[i__ + 1] + sx[
i__ + 2] * sy[i__ + 2] + sx[i__ + 3] * sy[i__ + 3] + sx[i__ +
4] * sy[i__ + 4];
/* L50: */
}
L60:
ret_val = stemp;
return ret_val;
} /* sdot_ */
/* Subroutine */ int sgemm_(char *transa, char *transb, integer *m, integer *
n, integer *k, real *alpha, real *a, integer *lda, real *b, integer *
ldb, real *beta, real *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer i__, j, l, info;
static logical nota, notb;
static real temp;
static integer ncola;
extern logical lsame_(char *, char *);
static integer nrowa, nrowb;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SGEMM 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 - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, ka ), where ka is
k when TRANSA = 'N' or 'n', and is m otherwise.
Before entry with TRANSA = 'N' or 'n', the leading m by k
part of the array A must contain the matrix A, otherwise
the leading k by m part of the array A must contain the
matrix A.
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 - REAL array of DIMENSION ( LDB, kb ), where kb is
n when TRANSB = 'N' or 'n', and is k otherwise.
Before entry with TRANSB = 'N' or 'n', the leading k by n
part of the array B must contain the matrix B, otherwise
the leading n by k part of the array B must contain the
matrix B.
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 - REAL .
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 - REAL array of DIMENSION ( LDC, n ).
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n matrix
( alpha*op( A )*op( B ) + beta*C ).
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.
Set NOTA and NOTB as true if A and B respectively are not
transposed and set NROWA, NCOLA and NROWB as the number of rows
and columns of A and the number of rows of B respectively.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
nota = lsame_(transa, "N");
notb = lsame_(transb, "N");
if (nota) {
nrowa = *m;
ncola = *k;
} else {
nrowa = *k;
ncola = *m;
}
if (notb) {
nrowb = *k;
} else {
nrowb = *n;
}
/* Test the input parameters. */
info = 0;
if (! nota && ! lsame_(transa, "C") && ! lsame_(
transa, "T")) {
info = 1;
} else if (! notb && ! lsame_(transb, "C") && !
lsame_(transb, "T")) {
info = 2;
} else if (*m < 0) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*k < 0) {
info = 5;
} else if (*lda < max(1,nrowa)) {
info = 8;
} else if (*ldb < max(1,nrowb)) {
info = 10;
} else if (*ldc < max(1,*m)) {
info = 13;
}
if (info != 0) {
xerbla_("SGEMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || (*alpha == 0.f || *k == 0) && *beta == 1.f) {
return 0;
}
/* And if alpha.eq.zero. */
if (*alpha == 0.f) {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
return 0;
}
/* Start the operations. */
if (notb) {
if (nota) {
/* Form C := alpha*A*B + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L50: */
}
} else if (*beta != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L60: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (b[l + j * b_dim1] != 0.f) {
temp = *alpha * b[l + j * b_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L70: */
}
}
/* L80: */
}
/* L90: */
}
} else {
/* Form C := alpha*A'*B + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * b[l + j * b_dim1];
/* L100: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L110: */
}
/* L120: */
}
}
} else {
if (nota) {
/* Form C := alpha*A*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L130: */
}
} else if (*beta != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L140: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (b[j + l * b_dim1] != 0.f) {
temp = *alpha * b[j + l * b_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L150: */
}
}
/* L160: */
}
/* L170: */
}
} else {
/* Form C := alpha*A'*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * b[j + l * b_dim1];
/* L180: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L190: */
}
/* L200: */
}
}
}
return 0;
/* End of SGEMM . */
} /* sgemm_ */
/* Subroutine */ int sgemv_(char *trans, integer *m, integer *n, real *alpha,
real *a, integer *lda, real *x, integer *incx, real *beta, real *y,
integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static real temp;
static integer lenx, leny;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SGEMV 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 - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL 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 - REAL array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
Before entry, the incremented array X must contain the
vector x.
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 - REAL .
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 - REAL array of DIMENSION at least
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
Before entry with BETA non-zero, the incremented array Y
must contain the vector y. On exit, Y is overwritten by the
updated vector y.
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.
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*lda < max(1,*m)) {
info = 6;
} else if (*incx == 0) {
info = 8;
} else if (*incy == 0) {
info = 11;
}
if (info != 0) {
xerbla_("SGEMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0.f && *beta == 1.f) {
return 0;
}
/*
Set LENX and LENY, the lengths of the vectors x and y, and set
up the start points in X and Y.
*/
if (lsame_(trans, "N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
First form y := beta*y.
*/
if (*beta != 1.f) {
if (*incy == 1) {
if (*beta == 0.f) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.f;
/* L10: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.f) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.f;
iy += *incy;
/* L30: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.f) {
return 0;
}
if (lsame_(trans, "N")) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (*incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.f) {
temp = *alpha * x[jx];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__] += temp * a[i__ + j * a_dim1];
/* L50: */
}
}
jx += *incx;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.f) {
temp = *alpha * x[jx];
iy = ky;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
y[iy] += temp * a[i__ + j * a_dim1];
iy += *incy;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
} else {
/* Form y := alpha*A'*x + y. */
jy = ky;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.f;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += a[i__ + j * a_dim1] * x[i__];
/* L90: */
}
y[jy] += *alpha * temp;
jy += *incy;
/* L100: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.f;
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += a[i__ + j * a_dim1] * x[ix];
ix += *incx;
/* L110: */
}
y[jy] += *alpha * temp;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of SGEMV . */
} /* sgemv_ */
/* Subroutine */ int sscal_(integer *n, real *sa, real *sx, integer *incx)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer i__, m, mp1, nincx;
/*
scales a vector by a constant.
uses unrolled loops for increment equal to 1.
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
*/
/* Parameter adjustments */
--sx;
/* Function Body */
if (*n <= 0 || *incx <= 0) {
return 0;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
sx[i__] = *sa * sx[i__];
/* L10: */
}
return 0;
/*
code for increment equal to 1
clean-up loop
*/
L20:
m = *n % 5;
if (m == 0) {
goto L40;
}
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
sx[i__] = *sa * sx[i__];
/* L30: */
}
if (*n < 5) {
return 0;
}
L40:
mp1 = m + 1;
i__2 = *n;
for (i__ = mp1; i__ <= i__2; i__ += 5) {
sx[i__] = *sa * sx[i__];
sx[i__ + 1] = *sa * sx[i__ + 1];
sx[i__ + 2] = *sa * sx[i__ + 2];
sx[i__ + 3] = *sa * sx[i__ + 3];
sx[i__ + 4] = *sa * sx[i__ + 4];
/* L50: */
}
return 0;
} /* sscal_ */
/* Subroutine */ int ssymm_(char *side, char *uplo, integer *m, integer *n,
real *alpha, real *a, integer *lda, real *b, integer *ldb, real *beta,
real *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer i__, j, k, info;
static real temp1, temp2;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SSYMM 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 - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, ka ), where ka is
m when SIDE = 'L' or 'l' and is n otherwise.
Before entry with SIDE = 'L' or 'l', the m by m part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading m by m upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading m by m lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
Before entry with SIDE = 'R' or 'r', the n by n part of
the array A must contain the symmetric matrix, such that
when UPLO = 'U' or 'u', the leading n by n upper triangular
part of the array A must contain the upper triangular part
of the symmetric matrix and the strictly lower triangular
part of A is not referenced, and when UPLO = 'L' or 'l',
the leading n by n lower triangular part of the array A
must contain the lower triangular part of the symmetric
matrix and the strictly upper triangular part of A is not
referenced.
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 - REAL 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 - REAL .
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 - REAL array of DIMENSION ( LDC, n ).
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n updated
matrix.
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.
Set NROWA as the number of rows of A.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(side, "L")) {
nrowa = *m;
} else {
nrowa = *n;
}
upper = lsame_(uplo, "U");
/* Test the input parameters. */
info = 0;
if (! lsame_(side, "L") && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (*m < 0) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldb < max(1,*m)) {
info = 9;
} else if (*ldc < max(1,*m)) {
info = 12;
}
if (info != 0) {
xerbla_("SSYMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0.f && *beta == 1.f) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.f) {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
return 0;
}
/* Start the operations. */
if (lsame_(side, "L")) {
/* Form C := alpha*A*B + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp1 = *alpha * b[i__ + j * b_dim1];
temp2 = 0.f;
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1];
temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1];
/* L50: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1]
+ *alpha * temp2;
} else {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
+ temp1 * a[i__ + i__ * a_dim1] + *alpha *
temp2;
}
/* L60: */
}
/* L70: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp1 = *alpha * b[i__ + j * b_dim1];
temp2 = 0.f;
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1];
temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1];
/* L80: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1]
+ *alpha * temp2;
} else {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
+ temp1 * a[i__ + i__ * a_dim1] + *alpha *
temp2;
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form C := alpha*B*A + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * a[j + j * a_dim1];
if (*beta == 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = temp1 * b[i__ + j * b_dim1];
/* L110: */
}
} else {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] +
temp1 * b[i__ + j * b_dim1];
/* L120: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (upper) {
temp1 = *alpha * a[k + j * a_dim1];
} else {
temp1 = *alpha * a[j + k * a_dim1];
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1];
/* L130: */
}
/* L140: */
}
i__2 = *n;
for (k = j + 1; k <= i__2; ++k) {
if (upper) {
temp1 = *alpha * a[j + k * a_dim1];
} else {
temp1 = *alpha * a[k + j * a_dim1];
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1];
/* L150: */
}
/* L160: */
}
/* L170: */
}
}
return 0;
/* End of SSYMM . */
} /* ssymm_ */
/* Subroutine */ int ssyrk_(char *uplo, char *trans, integer *n, integer *k,
real *alpha, real *a, integer *lda, real *beta, real *c__, integer *
ldc)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, l, info;
static real temp;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SSYRK 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 - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
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 - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - REAL array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
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.
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldc < max(1,*n)) {
info = 10;
}
if (info != 0) {
xerbla_("SSYRK ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (*alpha == 0.f || *k == 0) && *beta == 1.f) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.f) {
if (upper) {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
} else {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/* Form C := alpha*A*A' + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L90: */
}
} else if (*beta != 1.f) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L100: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0.f) {
temp = *alpha * a[j + l * a_dim1];
i__3 = j;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L110: */
}
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L140: */
}
} else if (*beta != 1.f) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L150: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0.f) {
temp = *alpha * a[j + l * a_dim1];
i__3 = *n;
for (i__ = j; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
}
} else {
/* Form C := alpha*A'*A + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * a[l + j * a_dim1];
/* L190: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L200: */
}
/* L210: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
temp = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * a[l + j * a_dim1];
/* L220: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L230: */
}
/* L240: */
}
}
}
return 0;
/* End of SSYRK . */
} /* ssyrk_ */
/* Subroutine */ int strsm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, real *alpha, real *a, integer *lda, real *b,
integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, k, info;
static real temp;
static logical lside;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
/*
Purpose
=======
STRSM solves one of the matrix equations
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
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 - REAL .
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
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 - REAL 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.
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("STRSM ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*inv( A )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L30: */
}
}
for (k = *m; k >= 1; --k) {
if (b[k + j * b_dim1] != 0.f) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L70: */
}
}
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
if (b[k + j * b_dim1] != 0.f) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__3 = *m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form B := alpha*inv( A' )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = *alpha * b[i__ + j * b_dim1];
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L110: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp = *alpha * b[i__ + j * b_dim1];
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L140: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L150: */
}
/* L160: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*inv( A ). */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L170: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (a[k + j * a_dim1] != 0.f) {
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L180: */
}
}
/* L190: */
}
if (nounit) {
temp = 1.f / a[j + j * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L200: */
}
}
/* L210: */
}
} else {
for (j = *n; j >= 1; --j) {
if (*alpha != 1.f) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L220: */
}
}
i__1 = *n;
for (k = j + 1; k <= i__1; ++k) {
if (a[k + j * a_dim1] != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L230: */
}
}
/* L240: */
}
if (nounit) {
temp = 1.f / a[j + j * a_dim1];
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L250: */
}
}
/* L260: */
}
}
} else {
/* Form B := alpha*B*inv( A' ). */
if (upper) {
for (k = *n; k >= 1; --k) {
if (nounit) {
temp = 1.f / a[k + k * a_dim1];
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L270: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
if (a[j + k * a_dim1] != 0.f) {
temp = a[j + k * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L280: */
}
}
/* L290: */
}
if (*alpha != 1.f) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
;
/* L300: */
}
}
/* L310: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
temp = 1.f / a[k + k * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L320: */
}
}
i__2 = *n;
for (j = k + 1; j <= i__2; ++j) {
if (a[j + k * a_dim1] != 0.f) {
temp = a[j + k * a_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L330: */
}
}
/* L340: */
}
if (*alpha != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
;
/* L350: */
}
}
/* L360: */
}
}
}
}
return 0;
/* End of STRSM . */
} /* strsm_ */
/* Subroutine */ int xerbla_(char *srname, integer *info)
{
/* Format strings */
static char fmt_9999[] = "(\002 ** On entry to \002,a6,\002 parameter nu"
"mber \002,i2,\002 had \002,\002an illegal value\002)";
/* Builtin functions */
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Subroutine */ int s_stop(char *, ftnlen);
/* Fortran I/O blocks */
static cilist io___60 = { 0, 6, 0, fmt_9999, 0 };
/*
-- LAPACK auxiliary routine (preliminary version) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
XERBLA is an error handler for the LAPACK routines.
It is called by an LAPACK routine if an input parameter has an
invalid value. A message is printed and execution stops.
Installers may consider modifying the STOP statement in order to
call system-specific exception-handling facilities.
Arguments
=========
SRNAME (input) CHARACTER*6
The name of the routine which called XERBLA.
INFO (input) INTEGER
The position of the invalid parameter in the parameter list
of the calling routine.
*/
s_wsfe(&io___60);
do_fio(&c__1, srname, (ftnlen)6);
do_fio(&c__1, (char *)&(*info), (ftnlen)sizeof(integer));
e_wsfe();
s_stop("", (ftnlen)0);
/* End of XERBLA */
return 0;
} /* xerbla_ */
cilist
Definition: f2c.h:45